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Business Plan Math - Reading Quiz

11th - 12th grade.

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What is the term used for a 3-5 year forecast of your income and expenses?

Financial model

Profits and losses

Spreadsheet

What is an example of a monthly, recurring expense?

Lease down payment

What is the type of pricing determined largely by what other companies in your industry are charging?

Competitors' pricing

Value-based pricing

Simple pricing

Cost-plus pricing

What is the rate at which the business grows or increases revenue from sales?

Profit margin

Monthly profit

Growth percentage

Examples of direct costs are:

Utilities and rent

Labor and material costs

Pricing your product based how a customer perceives the product is called:

Sales revenue is calculated by:

Number of sales multiplied by average customer sale dollar amount

Sales price multiplied by cost of goods sold

Number of sales multiplied by cost of goods sold

True or False: Net profit is greater than gross profit.

Starting a company in which you only spend money that is absolutely necessary at each point in time is called a:

Lean startup

Sole proprietor

Growth startup

What is the description of each axis on a breakeven chart?

Profit and volume

Sales and expenses

Direct costs and indirect costs

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Chapter 13: Solutions to Exercises

13.1: calculating interest and principal components.

• A lump sum of $100,000 is placed into an investment annuity to make end-of-month payments for 20 years at 4% compounded semi-annually. a) What is the size of the monthly payment? b) Calculate the principal portion of the 203rd payment. c) Calculate the interest portion of the 76th payment. d) Calculate the total interest received in the fifth year. e) Calculate the principal portion of the payments made in the seventh year.

a) What is the size of the monthly payment?

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 20 \times 12 = 240 \;\text{payments}[/latex] [latex]I/Y = 4[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]PV = -100,\!000[/latex] [latex]FV = 0[/latex] [latex]PV = -100,\!000[/latex] [latex]CPT\; PMT =\$604.2464648[/latex]

Make sure to reinput PMT =$604.25 (Input as a positive value rounded to 2 decimal places).

b)  Calculate the principal portion of the 203rd payment.

2nd AMORT P1 = 203 P2 = 203 ↓ ↓ PRN = $533.03

c) Calculate the interest portion of the 76th payment.

2nd AMORT P1 = 76 P2 = 76 ↓ ↓ ↓ INT = $253.73

d)  Calculate the total interest received in the fifth year.

Year 1: payments 1 – 12 Year 2: payments 13 – 24 Year 3: payments 25 – 36 Year 4: payments 37 – 48 Year 5: payments 49 – 60

2nd AMORT P1 = 49           (Starting with payment 49) P2 = 60          (Ending with payment 60) ↓ ↓ ↓ INT = $3,332.61

e) Calculate the principal portion of the payments made in the seventh year .

Year 1: payments 1 – 12 Year 2: payments 13 – 24 Year 3: payments 25 – 36 Year 4: payments 37 – 48 Year 5: payments 49 – 60 Year 6: payments 61 – 72 Year 7: payments 73 – 84

2nd AMORT P1 = 73 P2 = 84 ↓ ↓ PRN = $4,241.39

• At the age of 54, Hillary just finished all the arrangements on her parents’ estate. She is going to invest her $75,000 inheritance at 6.25% compounded annually until she retires at age 65, and then she wants to receive month-end payments for the following 20 years. The income annuity is expected to earn 3.85% compounded annually. a) What are the principal and interest portions for the first payment of the income annuity? b) What is the portion of interest earned on the payments made in the second year of the income annuity? c) By what amount is the principal of the income annuity reduced in the fifth year?

a) What are the principal and interest portions for the first payment of the income annuity?

Step 1:   Find [latex]FV[/latex].

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 11 \times 1 = 11 \;\text{payments}[/latex] [latex]I/Y = 6.25[/latex] [latex]P/Y = 1[/latex] [latex]C/Y = 1[/latex] [latex]PV = 75,\!000[/latex] [latex]PMT = 0[/latex] [latex]PV = 75,\!000[/latex] [latex]CPT\; FV =-\$146,\!109.88[/latex]

Step 2:  Find [latex]PMT[/latex].

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 20 \times 12 = 240 \;\text{payments}[/latex] [latex]I/Y = 3.85[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 1[/latex] [latex]PV = \$146,\!109.88[/latex] [latex]FV = 0[/latex] [latex]PV = \$146,\!109.88[/latex] [latex]CPT\; PMT =-868.83224[/latex]

Make sure to reinput PMT = -868.83 (Input as a negative value rounded to 2 decimal places).

2nd AMORT P1 = 1 P2 = 1 ↓ ↓ PRN = $408.13 INT = $460.70

b) What is the portion of interest earned on the payments made in the second year of the income annuity?

2nd AMORT P1 = 13 P2 = 24 ↓ ↓ ↓ INT = $5,250.65

c)   By what amount is the principal of the income annuity reduced in the fifth year?

2nd AMORT P1 = 49 P2 = 60 ↓ ↓ PRN = $5,796.37

• Art Industries just financed a $10,000 purchase at 5.9% compounded annually. It fixes the loan payment at $300 per month. a) How long will it take to pay the loan off? b) What are the interest and principal components of the 16th payment? c) For tax purposes, Art Industries needs to know the total interest paid for payments 7 through 18. Calculate the amount.

a) How long will it take to pay the loan off?

[latex]I/Y = 5.9[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 1[/latex] [latex]PV = 10,\!000[/latex] [latex]PMT=-300[/latex] [latex]FV= 0[/latex] [latex]CPT\; N =36.402469\;\text{rounded up to}\; 37\;\text{ monthly payments}[/latex]

[latex]\begin{align} \text{Number of years}&=\frac{37}{12}\\ &= 3.08\overline{3}\\ &=3\;\text{years and}\; 0.08\overline{3}\times 12=1\; \text{month} \end{align}[/latex]

3 years, 1 month

b) What are the interest and principal components of the 16th payment?

2nd AMORT P1 = 16 P2 = 16 ↓ ↓ PRN = $270.84 INT = $29.16

c) For tax purposes, Art Industries needs to know the total interest paid for payments 7 through 18. Calculate the amount.

2nd AMORT P1 = 7 P2 = 18 ↓ ↓ ↓ INT = $403.33

13.2: Calculating the Final Payment

• Semi-annual payments are to be made against a $97,500 loan at 7.5% compounded semi-annually with a 10-year amortization. a) What is the amount of the final payment? b) Calculate the principal and interest portions of the payments in the final two years.

Step 1 : Find the regular payment.

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 10 \times 2 = 20 \;\text{payments}[/latex] [latex]I/Y = 7.5[/latex] [latex]P/Y = 2[/latex] [latex]C/Y = 2[/latex] [latex]PV = 97,\!500[/latex] [latex]FV = 0[/latex] [latex]CPT\; PMT = -\$7,\!016.30449[/latex]

Make sure to reinput PMT = -7,016.30 (Input as a negative value rounded to 2 decimal places).

Step 2: Use the AMORT function to find the BAL on the last line (payment 20).

2nd AMORT P1 = 20 P2 = 20 ↓ BAL = $0.130277

Step 3: Find the Final Payment

Final Payment = $7,016.30 + $0.130277 = $7,016.43.

Year 9: payments 17-18 Year 10: payments 19-20

2nd AMORT P1 = 17 P2 = 20 ↓ BAL = $0.130277 (*added to payment of $7,016.30 = $7,016.43) PRN = $25,619.18861 (* add BAL:  $25,619.18861 + $0.130277 = $25,619.32) INT = $2,446.011387

Therefore, PRN = $25,619.32; INT = $2,446.01.

• A $65,000 trust fund is set up to make end-of-year payments for 15 years while earning 3.5% compounded quarterly. a) What is the amount of the final payment? b) Calculate the principal and interest portion of the payments in the final three years.

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 15 \times 1 = 15 \;\text{payments}[/latex] [latex]I/Y = 3.5[/latex] [latex]P/Y = 1[/latex] [latex]C/Y = 4[/latex] [latex]PV = 65,\!000[/latex] [latex]FV = 0[/latex] [latex]CPT\; PMT = -\$5,\!662.190832[/latex]

Make sure to reinput PMT = -5,662.19 (Input as a negative value rounded to 2 decimal places).

Step 2: Use the AMORT function to find the BAL on the last line (payment 15)

2nd AMORT P1 = 15 P2 = 15 ↓ BAL = $0.016114

Final Payment = $5,662.19 + $0.016114 = $5,662.21.

2nd AMORT P1 = 13 P2 = 15 ↓ BAL = $0.016114 (*added to payment of $5,662.19 = $5,662.21) PRN = $15,849.40807 (* add BAL:  $15,849.40807 + $0.016114 = $15,849.42) INT = $1,137.161928

Therefore, PRN = $15,849.42; INT = $1,137.16.

• Mirabel Wholesale has a retail client that is struggling and wants to make instalments against its most recent invoice for $133,465.32. Mirabel works out a plan at 12.5% compounded monthly with beginning-of-month payments for two years. a) What will be the amount of the final payment? b) Calculate the principal and interest portions of the payments for the entire agreement.

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 2 \times 12= 24 \;\text{payments}[/latex] [latex]I/Y = 12.5[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 12[/latex] [latex]PV = 133,\!465.32[/latex] [latex]FV = 0[/latex] [latex]CPT\; PMT = -\$6,\!248.793434[/latex]

Make sure to reinput PMT = -6,248.79 (Input as a negative value rounded to 2 decimal places).

Step 2: Use the AMORT function to find the BAL on the last line (payment 24)

2nd AMORT P1 = 24 P2 = 24 ↓ BAL = $0.093078

Final Payment = $6,248.79 + $0.093078 = $6,248.88.

2nd AMORT P1 = 1 P2 = 24 ↓ BAL = $0.093078 (*added to payment of $6,248.79 = $6,248.88) PRN = $133,465.2269 (* add BAL:  $133,465.2269 + $0.093078 = $133,465.32) INT = $16,505.73308

Therefore, PRN = $133,465.32; INT = $16,505.73.

13.3: Amortization Schedules

• A farmer purchased a John Deere combine for $369,930. The equipment dealership sets up a financing plan to allow for end-of-quarter payments for the next two years at 7.8% compounded monthly. Construct a complete amortization schedule and calculate the total interest.

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 2 \times 4= 8 \;\text{payments}[/latex] [latex]I/Y = 7.8[/latex] [latex]P/Y = 4[/latex] [latex]C/Y = 12[/latex] [latex]PV = 369,\!930[/latex] [latex]FV = 0[/latex] [latex]CPT\; PMT = -\$50,\!417.92645[/latex]

Make sure to reinput PMT = -50,417.93 (Input as a negative value rounded to 2 decimal places).

Step 2: Use the AMORT function to fill out the table.

Step 3: Adjust for the “missing pennies” (noted in bold italics ) and total the interest.

• Ron and Natasha had Oasis Leisure and Spa install an in-ground swimming pool for $51,000. The financing plan through the company allows for end-of-month payments for two years at 6.9% compounded quarterly. Ron and Natasha instruct Oasis to round their monthly payment upward to the next dollar amount evenly divisible by $500. Create a schedule for the first three payments, payments seven through nine, and the last three payments.

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 2 \times 12= 24 \;\text{payments}[/latex] [latex]I/Y = 6.9[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 4[/latex] [latex]PV = 51,\!000[/latex] [latex]FV = 0[/latex] [latex]CPT\; PMT = -\$2,\!280.18[/latex]

Make sure to reinput PMT = – $2,500 ($2,280.18 rounded up to $2,500).

Step 2 : Recalculate N with new PMT.

[latex]I/Y = 6.9[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 4[/latex] [latex]PV = 51,\!000[/latex] [latex]PMT = -2,\!500[/latex] [latex]FV = 0[/latex] [latex]CPT\; N = 21.753021\; \text{rounded up to}\; 22\; \text{monthly payments}[/latex]

Step 3:  Use the AMORT function to fill out the table.

Step 4: Adjust for the “missing pennies” (noted in bold italics ) and total the interest.

• Hillary acquired an antique bedroom set recovered from a European castle for $118,000. She will finance the purchase at 7.95% compounded annually through a plan allowing for payments of $18,000 at the end of every quarter. a) Create a complete amortization schedule and indicate her total interest paid. b) Recreate the complete amortization schedule if Hillary pays two additional top-up payments consisting of 10% of the principal remaining after her third payment as well as her fifth payment. What amount of interest does she save?

Step 1: Find [latex]N[/latex].

[latex]I/Y = 7.95[/latex] [latex]P/Y = 4[/latex] [latex]C/Y = 1[/latex] [latex]PMT = -18,\!000[/latex] [latex]PV = 118,\!000[/latex] [latex]FV = 0[/latex] [latex]CPT\; N = 7.076614\; \text{rounded up to}\; 8\; \text{quarterly payments}[/latex]

Step 2:  Use the AMORT function to fill out the table.

Step 1:  Use the AMORT function to fill out the table.

*The balance after the third payment was $69,918.68.  10% of this amount is $6,991.87. **The balance after the fifth payment was $29,032.76. 10% of this amount is $2,903.28.

Step 2: Adjust for the “missing pennies” (noted in bold italics ) and total the interest.

From Question 18a, amount of interest paid was $9,391.27. Interest Saved = $9,391.27 − $8,695.87 = $695.40.

13.4: Special Application – Mortgages

• Three years ago, Phalatda took out a mortgage on her new home in Kelowna for $628,200 less a $100,000 down payment at 6.49% compounded semi-annually. She is making monthly payments over her three-year term based on a 30-year amortization. At renewal, she is able to obtain a new mortgage on a four-year term at 6.19% compounded semi-annually while continuing with monthly payments and the original amortization timeline. Calculate the following: a) Interest and principal portions in the first term. b) New mortgage payment amount in the second term. c) Balance remaining after the second term.

Step 1 : Find the initial payment.

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 30 \times 12 = 360 \;\text{payments}[/latex] [latex]I/Y = 6.49[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV = 628,\!200 − 100,\!000 = 528,\!200[/latex] [latex]CPT\; PMT =-\$3,\!305.288742[/latex]

Make sure to reinput PMT = -3,305.29 (Input as a negative value rounded to 2 decimal places).

Step 2: Use the AMORT function to find the BAL on the after the first term (payment 1-36).

2nd AMORT P1 = 1 P2 = 36 ↓ BAL = $508,947.54

2nd AMORT P1 = 1 P2 = 36 ↓ ↓ PRN = $19,252.46 INT = $99,737.98

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 27 \times 12 = 324 \;\text{payments}[/latex] [latex]I/Y = 6.19[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV = 508,\!947.54[/latex] [latex]CPT\; PMT =-\$3,\!211.32429[/latex]

Make sure to reinput PMT = -3,211.32 (Input as a negative value rounded to 2 decimal places).

Use the AMORT function to find the BAL on the after the second term (payment 1-48).

2nd AMORT P1 = 1 P2 = 48 ↓ BAL = $475,372.69

• The Verhaeghes have signed a three-year closed fixed rate mortgage with a 20-year amortization and monthly payments. They negotiated an interest rate of 4.84% compounded semi-annually. The terms of the mortgage allow for the Verhaeghes to make a single top-up payment at any one point throughout the term. The mortgage principal was $323,000 and 18 months into the term they made one top-up payment of $20,000. a)What is the balance remaining at the end of the term? b)By what amount was the interest portion reduced by making the top-up payment?

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 20 \times 12 = 240 \;\text{payments}[/latex] [latex]I/Y = 4.84[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV = 323,\!000[/latex] [latex]CPT\; PMT =-\$2,\!094.701842[/latex]

Make sure to reinput PMT = -2,094.70 (Input as a negative value rounded to 2 decimal places).

Step 2: Use the AMORT function to find the BAL on the after the first 18 months.

2nd AMORT P1 = 1 P2 = 18 ↓ BAL = $308,009.80

  Step 3: Find New Balance after $20,000 top-up payment.

New Balance = $308,009.80 − $20,000 = $288,009.80. Reinput PV = $288,009.80.

Step 4: Use the AMORT function to find the BAL on the after the last 18 months of the first term.

2nd AMORT P1 = 1 P2 = 18 ↓ BAL = $270,417.34

Step 1: Find Original BAL paid without top-up payment (payments 1-36).

Reinput PV = $323,000

2nd AMORT P1 = 1 P2 = 36 ↓ BAL = $291,904.76

Step 2: Find Interest Difference.

[latex]\begin{align} \text{Interest Difference}&=\$291,\!904.76 − \$270,\!417.34 − \$20,\!000\\ &= \$1,\!487.42 \end{align}[/latex]

• Fifteen years ago, Clarissa’s initial principal on her mortgage was $408,650. She set up a 30-year amortization, and in her first 10-year term of monthly payments her mortgage rate was 7.7% compounded semi-annually. Upon renewal, she took a further five-year term with monthly payments at a mortgage rate of 5.69% compounded semi-annually. Today, she renews the mortgage but shortens the amortization period by five years when she sets up a three-year closed fixed rate mortgage of 3.45% compounded semi-annually with monthly payments. What principal will she borrow in her third term and what is the remaining balance at the end of the term? What total interest portion and principal portion will she have paid across all 18 years?

Step 1 : Find the initial payment for 10-year term.

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 30 \times 12 = 360 \;\text{payments}[/latex] [latex]I/Y = 7.7[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV = 408,\!650[/latex] [latex]CPT\; PMT =-\$2,\!879.565159[/latex]

Make sure to reinput PMT = -2,879.57 (Input as a negative value rounded to 2 decimal places).

  Step 2: Use the AMORT function to find the BAL on the after the 10-year term (payments 1-120).

2nd AMORT P1 = 1 P2 = 120 ↓ BAL = $355,303.81

Step 3 : Find the payment for 5-year term.

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 20 \times 12 = 240 \;\text{payments}[/latex] [latex]I/Y = 5.69[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV = 355,\!303.81[/latex] [latex]CPT\; PMT =-\$2,\!468.979621[/latex]

Make sure to reinput PMT = -2,468.98 (Input as a negative value rounded to 2 decimal places).

Step 4: Use the AMORT function to find the BAL on the after the 5-year term (payments 1-120).

2nd AMORT P1 = 1 P2 = 60 ↓ BAL = $299,756.24

Step 5 : Find the payment for 3-year term with amortization period shortened by 5 years. Number of years remaining = 15 – 5 = 10.

[latex]N = (\text{Number of Years}) \times (\text{Payments Per Year})[/latex] [latex]N = 10 \times 12 = 120 \;\text{payments}[/latex] [latex]I/Y = 3.45[/latex] [latex]P/Y = 12[/latex] [latex]C/Y = 2[/latex] [latex]FV = 0[/latex] [latex]PV =299,\!756.24[/latex] [latex]CPT\; PMT =-\$2,\!953.710318[/latex]

Make sure to reinput PMT = -2,953.71 (Input as a negative value rounded to 2 decimal places).

Step 6:   Use the AMORT function to find the BAL on the after the 3-year term (payments 1-36).

2nd AMORT P1 = 1 P2 = 36 ↓ BAL = $220,328.74

Start of 3rd term principal = $299,756.24. Remaining balance at end of 3rd term = $220,328.74.

[latex]\begin{align} \text{Total principal across all}\;18\;\text{years}&=\$408,\!650 - \$220,\!328.74\\ &= \$188,\!321.26 \end{align}[/latex]

[latex]\text{Total interest across all}\;18\;\text{years}[/latex] [latex]=(120 \times 2,\!879.57) + (60 \times 2,\!468.98) + (36 \times 2,\!953.71) - 188,\!321.26[/latex] [latex]= \$411,\!499.50[/latex]

Image Description

Figure 13.1.2: Timeline: Deferral period from age 54 until age 65 at 6.25% compounded annually. Starting at age 55, 20 years end of month payments of PMT at 3.85% compounded annually. $75,000 at age 54 brought to age 65 as FV. At age 65 the FV becomes the PV for the stream of PMT’s brought back to age 65. [ Back to Figure 13.1.2 ]

Business Math: A Step-by-Step Handbook Abridged Copyright © 2022 by Sanja Krajisnik; Carol Leppinen; and Jelena Loncar-Vines is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Questions and answers, which of the following is not a key aspect of business math.

• Developing marketing strategies (correct)
• Understanding percentages
• Calculating profit and loss
• Balancing the books

If a company's revenue is $500,000 and the total cost of producing goods or services is $350,000, what is the company's profit?

• $150,000 (correct)

If a company's market share increased by 20% last year, and its initial market share was 30%, what is its current market share?

• 36% (correct)

If a company's credit side is $100,000 and its debit side is $95,000, what must be done to balance the books?

<p>Increase the debit side by $5,000</p> Signup and view all the answers

If a company borrows $100,000 at an annual interest rate of 6% compounded annually, how much interest will it pay in the first year?

<p>$6,000</p> Signup and view all the answers

If a company's revenue increased by 15% from the previous year, and its expenses increased by 10%, what is the impact on the company's profitability?

<p>Profitability increased</p> Signup and view all the answers

Which of the following is NOT a primary application of business math?

<p>Developing algorithms for natural language processing</p> Signup and view all the answers

If a company has a current inventory level of 5,000 units, and the expected monthly demand is 1,200 units, what is the optimal reorder point if the lead time for replenishment is 2 months and the company wants to maintain a safety stock of 500 units?

<p>3,400 units</p> Signup and view all the answers

If a company's current ratio (current assets / current liabilities) is 1.5, and its quick ratio (cash + marketable securities + accounts receivable / current liabilities) is 0.8, what is the approximate value of its inventory as a fraction of its current assets?

<p>2/3</p> Signup and view all the answers

If a company's fixed costs are $50,000 per month, and its variable costs are $10 per unit produced, what is the breakeven point in units if the selling price is $25 per unit?

<p>3,000 units</p> Signup and view all the answers

A company is considering two mutually exclusive projects. Project A has an initial investment of $100,000 and is expected to generate cash flows of $30,000 per year for 5 years. Project B has an initial investment of $150,000 and is expected to generate cash flows of $50,000 per year for 4 years. If the company's required rate of return is 10%, which project should it choose based on the net present value (NPV) method?

<p>Project B</p> Signup and view all the answers

A company is considering three different pricing strategies for a new product. If the price is set at $100, the expected demand is 10,000 units. If the price is set at $80, the expected demand is 15,000 units. If the price is set at $60, the expected demand is 20,000 units. The variable cost per unit is $40, and the fixed costs are $200,000. Which pricing strategy will maximize the company's profit?

<p>$80 pricing strategy</p> Signup and view all the answers

Study Notes

Business math.

Business math refers to the practical application of mathematical concepts and principles to business situations. It is concerned with solving problems related to accounting, finance, economics, management, marketing, and other areas within commercial operations. Here are some key aspects of business math:

Calculating Profit and Loss

Profit and loss calculations are crucial in business math. They help determine the efficiency of a business and the potential for future growth. Profit is calculated by subtracting the total cost of producing goods or services from the revenue generated.

Balancing the Books

Accounting involves balancing the books, which is a fundamental part of business math. This means ensuring that the sum of the debit and credit sides of a company's financial records are equal. Balancing the books is necessary for accurate financial reporting and decision-making.

Percentages

Percentages are used frequently in business math. They help in calculating the increase or decrease in a company's profitability, market share, or other key performance indicators. Understanding percentages is crucial for making informed decisions in business.

Interest Rates

Interest rates play a significant role in business math. They help businesses understand the cost of borrowing money, the potential return on investments, and the overall financial health of a company. Interest rates are used in various financial calculations, such as calculating the total cost of a loan or assessing the profitability of an investment.

Cost Accounting

Cost accounting involves analyzing and allocating costs to different products or services within a business. This helps businesses understand their costs and pricing strategies. Cost accounting is a critical part of business math, as it helps companies make informed decisions about product pricing and resource allocation.

Inventory Management

Inventory management is another aspect of business math. It involves tracking the flow of inventory, predicting future demand, and managing the cost of holding inventory. Effective inventory management is essential for maintaining customer satisfaction and minimizing costs.

Financial Analysis

Financial analysis is a complex area of business math. It involves interpreting financial statements, calculating financial ratios, and making predictions about future financial performance. Financial analysis is crucial for making informed decisions about a company's future growth and profitability.

Decision Making

Business math provides the tools and techniques necessary for making informed decisions in business. By understanding the principles of business math, businesses can make better decisions about pricing, production, inventory, and other critical aspects of their operations.

In conclusion, business math is a vital aspect of commercial operations. It provides the tools and techniques necessary for making informed decisions, managing finances, and assessing performance. Understanding business math is essential for any individual or organization involved in commercial activities.

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Test your knowledge of key aspects of business math including profit and loss calculations, balancing the books, percentages, interest rates, cost accounting, inventory management, financial analysis, and decision making. This quiz covers essential concepts for individuals and organizations involved in commercial activities.

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Finance Test

Assess your knowledge on finance concepts, definitions, and calculations

This Finance Test is designed to help you assess your knowledge of important finance concepts, terminology definitions, and frequently used calculations. We strongly encourage any students who are planning or are beginning their FMVA certification program  to take this test to determine whether you will need to take the prerequisite finance courses including Reading Financial Statements ,  Introduction to Corporate Finance , and Math for Corporate Finance . This is also a useful resource for employers to examine the technical knowledge of the candidates during a finance interview.

If you pass this test with 80% or above (16 questions or more), it is likely that you have a strong background in finance and are good to go ahead with our core courses!

Finance Test Questions

• The discount rate is always higher when you invest now than in the future
• The discount rate is always higher when you invest in the future than now
• The money you have now is worth less today than an identical amount you would receive in the future
• The money you have now is worth more today than an identical amount you would receive in the future
• FV = PV/(1+r)^n
• FV = PV/(1+r)*n
• FV = PV x (1+r)^n
• FV = PV x (1+r)*n

• An investment that has no definite end and a stream of cash payments that continues forever
• A stream of cash flows that start one year from today and continue while growing by a constant growth rate
• A series of equal payments at equal time periods and guaranteed for a fixed number of years
• A series of unequal payments at equal time periods which are guaranteed for a fixed number of years

• The amount borrowed by the issuer of the bond and returned to the investors when the bond matures
• The overall return earned by the bond investor when the bond matures
• The difference between the amount borrowed by the issuer of bond and the amount returned to investors at maturity
• The size of the coupon investors receive on an annual basis
• Trading at par
• Trading at a premium
• Trading at a discount
• Trading below par
• Coupon Rate > Current Yield > Yield to Maturity
• Coupon Rate
• Coupon Rate = Current Yield = Yield to Maturity
• The cash flows that occur earlier are more valuable than cash flows that occur later
• The cash flows that occur earlier are less valuable than cash flows that occur later
• The longer the time cash flows are invested, the more valuable they are in the future
• The future value of cash flows are always higher than the present value of the cash flows
• The market value of equity of the business
• The book value of equity of the business
• The entire value of the business without giving consideration to its capital structure
• The entire value of the business considering its capital structure
• Total assets/Net debt x Cost of debt + Total assets/Equity x Cost of equity
• Net debt/Equity x Cost of debt + Equity/Net debt x Cost of equity
• Net debt x Cost of debt + Equity x Cost of equity
• Net debt/Total assets x Cost of debt + Equity/Total assets x Cost of equity
• Private equity funds are pools of capital invested in companies which represent an opportunity for high rate of return
• Exit strategies for private equity funds include Initial Public Offerings (IPOs) and leveraged buyout (LBO)
• Venture capital is an example of private equity funds
• Private equity funds are usually invested for unlimited time periods
• Best efforts
• Firm commitment
• All-or-none
• Full-purchase
• Equity > Subordinated debt > Senior debt
• Suborindated debt > Senior debt > Equity
• Senior debt > Subordinated debt > Equity
• Senior debt > Equity > Subordinated debt
• Repayment of long-term debt
• Issuance of equity
• Investments in businesses
• Payment of dividends
• Equity Capital + Retained Earnings
• Equity Capital - Total Liabilities
• Total Assets - Total Liabilities
• Current Assets - Current Liabilities
• Goodwill needs to be evaluated for impairment yearly
• Goodwill is treated as a tangible asset in accounting
• Goodwill is a result of purchasing a company for a price higher than the fair market value of the target company's net assets
• Goodwill can be comprised of things such as good reputation, loyal client base, and brand recognition

More about CFI

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CFI is the official global provider of the  Financial Modeling and Valuation Analyst (FMVA)™ certification program , designed to transform anyone into a world-class financial analyst. Enroll now to gain the skills you need to take your career to the next level. Also, see all our valuation resources.

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	Click on the links under at the left to access feature-related activities. Unit Resources include WebQuests and other activities. To access the , select a chapter from the chapter pull-down menu at the left. To access the , select a unit from the unit pull-down menu at the left, then select a chapter from the chapter pull-down menu. Chapter Activities include Online Readiness Quizzes, Practice Tests, Visual Summaries, and more. Click an item at the left under the heading to access Multi-Media Links, Personal Finance Tools, a Spanish Glossary, and other resources. Click an item at the left to access teacher resources, including information about standards, answers to student activities, and more. These resources are available at no charge to users of the Teacher Wraparound Edition of Mathematics for Business and Personal Finance . At the prompt, please enter the user name " MBPF10 " and the password. The password is the last word on page TM 43 of the Teacher Wraparound Edition. 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Username: Password: StudentWorks Online with Advance Tracker Personal Tutor Radio Glencoe Podcasts Study-to-Go Career Clusters Textbook Resources Spanish Glossary Multi-Media Links Personal Finance Tools Tax Preparation Career Links Internet Activities Test-Taking Tips Job-Finding Tools and Tips Math Facts, Tools, and Tips Homework Hints Continuing Education Disability Support Links Graphing Calculator Labs Unit Resources Chapter Activities McGraw-Hill Professional Development Mini Clip Video Library Glencoe E-Zine Newsletter Teaching Today Career City National and State Standards Correlations Academic Standards Correlations Course Pacing Guide About Virtual Business PresentationPlus! Sample General Teaching Resources California Algebra Test Preparation and Practice Workbook Competitive Events  >  Please read our and before you explore our Web site. To report a technical problem with this Web site, please contact the . RETAILING Total Instructional Time The instructional time for RETAILING ranges from 24 hours (simulation exercises only) to 35 hours (simulation exercises, reading assignments , reading quizzes, and math quizzes) . You can configure your course to include or exclude reading assignments (3.7 hours) , reading quizzes (1.8 hours) and math quizzes (5.5 hours) . For instructions on how to configure your course, click here to access a series of videos to help you get your classroom up and running with Virtual Business. Prior to beginning work with RETAILING , students should sign in to their account at vb.KnowledgeMatters.com and go through the Tutorial. Lesson: Market Research Description. In this lesson, students learn that market research is critical to the success of a retail business. They begin by taking a survey of prospective customers to learn both product preferences and time of day preferences. Students then try to save some money by taking a similar survey but with reduced sample size. They are introduced to the mathematical concept of decreasing reliability of a survey as the sample size decreases. Students then explore the more sophisticated technique of analyzing survey data through segmentation. Finally, students use market research information to book radio advertising on a radio station that matches the demographic of their target customers. They run the simulation to try to achieve a specific profit goal. LEARNING OBJECTIVES Define market research Explain the difference between primary and secondary research Determine an adequate sample size for a survey Use segmentation to analyze survey results Use market research to make smart advertising decisions for a business Lesson: Product In this lesson, students begin as managers of a grocery store that is performing poorly. They look at their location and surrounding customers. Next, students use surveys to discover what products these customers want. Unfortunately, those aren’t the products their store is currently stocking. They replace a non-popular product with a popular one and see sales rise. Students then add a display to carry another popular product and and see an additional increase in sales. Finally, students take over an electronics store with similar problems and work to change the product offerings in pursuit of a specific weekly profit goal. Explain the importance of product choices in retailing Use surveys to determine most popular products Be able to change product mix and interpret sales results Manage product selection to achieve profit goals Lesson: Place In this lesson, students learn about location...location, location. Students begin by looking around their city. They identify the available square footage of buildings and the cost per square foot for the space. They compare costs per square foot for downtown versus suburban locations. Students next study what types of customers are near each location. Students also scout competitor locations within the city. Finally, students are asked to choose a location for their store. They run the simulation to try to reach a specific profit goal. If they are not successful, they try relocating their store. Understand the concept of cost per square foot Be able to compare amount and cost of space at different locations Assess the types of customers around a given location Assess potential locations given competitor locations Choose a store location that will yield a profit Lesson: Price In this lesson, students see how prices interact with the law of supply and demand to determine sales levels. They begin by reviewing the concepts of price, cost and margin. They then intentionally set prices quite high and observe that volume and profits drop. Next, they try setting prices very low. The observe greatly increased volume, but profits remain low due to slim margins. They try a price in between the initial price points and see how profit can be maximized. They see how profit can be plotted as a curve against price levels. Students then learn about the use of “loss leaders” to drive customers into stores with very low prices on attractive items. Finally, students are challenged to set prices for their store to meet a specific weekly profit goal. Explain the relationship between price, cost, and margin Explain how prices and sales volume is related Find a price that maximizes profit by generated reasonable volume and reasonable margins Define a “loss leader” Set prices across all products to achieve a profit goal Lesson: Promotion - Traditional Media In this lesson, students study the role of promotion in the marketing mix. They begin by finding their current weekly revenue on their Income Statement. Students then examine where their current customers are coming from -- a relatively small area of the city. To grow their customer base, they lease a billboard across town then compare their increase in revenue with the expense of the billboard. As an alternative to billboard promotion, they try running a one page ad in a newspaper circular. Students compare the revenue and expenses of the two different forms of promotion. Finally, students use promotions of their choosing to achieve a weekly revenue goal while keeping their promotional spending below a specified level. Understand promotion as a key element of the marketing mix Identify different types of promotion Track revenue and expenses associated with promotional activities Be able to compare efficiency of promotional campaigns Choose promotional means to achieve business goals Lesson: Promotion - Email In this lesson, students explore the use of Email as part of the marketing mix. Email is a relatively new, but extremely important, component of retail promotion. Students begin by looking atways to assemble target lists, including customer loyalty programs and purchased lists of Email addresses. They purchase a list and then make a strong offer to attract customers to sign up to receive more Emails. Students discover some perils of Email promotion by trying to send to the same list too frequently. This results in high spam reports that could shut down their Email capability. Finally, students use what they have learned about Email to promote their business successfully and reach a specific profit goal. Identify different sources of Email address lists Understand the importance of subject lines and offers in Email marketing Track and analyze Email response metrics Avoid spam reports by properly spacing Emails Use Email promotion to achieve profit goals Lesson: Staffing, Selling & Customer Service In this lesson, students take responsibility for staffing several types of retail stores. They begin in a grocery store and set conservative staffing levels for cashiers and stockers. They observe customers complaining about long lines and unstocked shelves. Students correct the staffing problem and observe increased profit on their Income Statement. Next students switch to an electronics store with high-ticket items that may require consultative selling. They use sales reports to find an item that is selling poorly. They then add salespeople and use the sales report to examine the subsequent increase in sales. Finally, students take on a sporting goods store with poor overall staffing and are challenged to staff the store to make a specific profit goal. Explain several different job functions within a retail store List the problems that can result from understaffing at each position Discuss why some retail establishments staff salespeople while others don’t Understand the expense/revenue tradeoff of staffing decisions Adequately staff a retail store to achieve a profit goal Lesson: Purchasing & Inventory Control In this lesson, students take over the role of purchasing manager in a retail business. They begin by intentionally purchasing a very low, conservative amount. They observe employees and customers complaining that they can’t find products they need. Next, they try purchasing very large amounts. This eliminates stock-outs, but now they observe certain products expiring. Students identify a specific product with a short shelf-life and set a custom purchasing level to eliminate expiration. Then students see how they can re-allocate space in their backroom to insure adequate stockpiles of products. Finally, students take control of all purchasing to try to run a full week with no products expiring and no complaints of customers being unable to find goods. Explain why purchasing is essential to a retail business Understand target inventory levels Explain the tradeoffs between purchasing too much and too little Set custom purchasing policies for rapidly expiring items Manage purchasing for efficiency and customer satisfaction Lesson: Merchandising In this lesson, students take over control of the layout of their store. Students begin by finding their weekly revenue on their Income Statement. Their revenue is good, but not great. They then identify whether certain items in the store are more likely “needs” or “impulse” items. Students are next introduced to the merchandising concept of putting needs in the back of the store to draw customers past impulse items. They rearrange a need item and watch as revenue increases. Students then place a “complementary” good next to the item it complements. Again, they experience rising sales. Finally, students are asked to apply these principles by rearranging their store layout to achieve a specific weekly revenue goal. Define merchandising in a retail store Identify items that are likely needs Identify items that are likely impulse purchases Identify items that are likely complementers Describe strategies for placing needs, impulse items, and complementers Use merchandising principles to improve the revenue of a business Lesson: Security & Risk Management In this lesson, students take on the role of security consultant for three different types of retail stores. They begin by looking at shrinkage (unexplained product shortages) at a grocery store. They identify which items are likely being shoplifted and reduce shoplifting by moving those items to more visible areas. Next, they look at an electronics store with high value items. They install an expensive scanner system and compare its cost with the shoplifting losses prevented. Finally, they head to a sporting goods store with medium value items and try to find an appropriate security system that will reduce losses within a certain budget. Explain the importance of security in a retail business Given different options for increasing security Analyze the cost-effectiveness of a security system Plan store security to achieve profit goals Lesson: Financing & Business Planning In this lesson, students will discover how to estimate their financing needs when starting a new business. They begin by figuring out how much they will need to spend on their building lease, equipment leases, and initial inventory. They then add in staffing costs to estimate their total start-up expenses. They take out a loan for the appropriate amount and start the business. After several weeks, they look at their Balance Sheet to see what their lowest cash position was. Using this information, they take on the challenge of starting an even larger retail store. Their goal is to borrow enough money to get the business off the ground while minimizing financing costs. Understand that most business require substantial financing (capital) to get started Be able to estimate start-up costs for a business Monitor cash levels to determine adequacy of financing Extrapolate from a small business to a larger business when estimating financing needs Acquire adequate financing to start a business while minimizing financing costs Lesson: Retailing Mogul - Unique City Per Class In this capstone project, students put to use the knowledge and skills they have learned in the lessons. They are challenged to build a retail grocery business from the ground up. They must choose a location, design their store layout, staff the business, choose products to carry, set prices, and more.  All students start in the same city and pursue a specific profit goal. By default, the class scoreboard is turned on so students can compare their profitability to others. The instructor can turn the scoreboard off. Understand the options for financing a start up Choose a suitable location for a business Design an effective retail floor plan Understands how to staff a retail business efficiently Plan merchandise selection and purchasing Use common financial statements to pursue a profit goal Understand the challenges and rewards of entrepreneurship Lesson: Extra Credit: Retailing Mega Mogul - Unique City Per Class In this extra credit project, students are free to explore all that the simulation has to offer. They can start grocery, sporting goods, and electronics stores. They can also start multiple stores of each type. This project is open-ended; students do not have a specific profit goal and can continue on as long as they desire. By default, the class scoreboard is turned on so instructors can use this project as a competition. Understand how to start a grocery business Understand how to start a sporting goods business Understand how to start an electronics business Compare and contrast running different types of retail businesses Manage the complexity of running multiple businesses Understand the importance of long-term planning and effort in growing a large business or businesses Lesson: Extra Credit: Turnaround In this extra credit project, students take over a struggling sporting goods retailer. The business has poor staffing, inappropriate product selection, and a terrible layout. Students are challenged to find and diagnose the problems. They then set about correcting them. Students learn that a single correction may not produce profits if other factors are not aligned. Eventually, students work through all the issues to achieve a profit.  By default, the class scoreboard is turned on so students can compete against each other for the title of “Turnaround King.” Identify problems within an existing business Formulate corrective actions Use financial statements and other reports to assess effectiveness of corrections Understand how corrections in one area of a business affect and depend on other areas of the business Restore an unprofitable business to profitability High School News & Events Support Home Privacy Policy Number line from -10 to 10 with all integers labeled Step 1: Draw a horizontal line representing the number line. Step 2: Label the left endpoint as -10 and the right endpoint as 10. Step 3: Mark all integers from -10 to 10 on the number line Financial Math test Summary of the financial math test. This Financial Math test assesses a candidate’s ability to perform mathematical computations essential for identifying and evaluating financial outcomes. The test helps you identify candidates who can perform these computations efficiently and accurately. Covered skills Linear programming and mathematical progression Time value of money Application of time value of money in business Use the Financial Math test to hire Financial analysts, financial researchers, financial officers, executives, members of in-house finance and accounts departments, and anyone else responsible for performing mathematical analysis and computations for financial decision-making. About the Financial Math test Sustainable growth for many businesses depends on accurate financial information. At the core of this financial information is financial math: functions, computations, and arithmetic related to financial information. Proper business decision-making is supported by various mathematical analyses and computations. High-quality financial mathematics is a hallmark of high-quality financial positions. To find suitable candidates for your organization, this screening test uses practical, scenario-based questions that ask candidates to solve financial math problems that regularly come up when handling finance-related matters, such as computation of present and future value, net present value, internal rate of return, real and nominal rate of return, and products leading to profit maximization. Candidates performing well on this Financial Math test will possess a good understanding of financial math and help your organization solve complicated finance-related problems and computations. Successful candidates will provide valuable input for your company’s financial decisions. All Financial Math test questions can be solved without using a calculator, but given the time constraints, access to a calculator is highly recommended for all candidates taking this test. The test is made by a subject-matter expert Abdul is a chartered accountant and certified ISO 31000 risk manager with over 15 years of experience managing other accountants and staff in many businesses, large and small. Abdul also has an MBA with significant consulting experience across business sectors, including oil and gas, pharmaceuticals, food, and education. He has worked as a university lecturer in accounting, finance, and tax-related subjects for more than five years and currently works on complex risk management policies as a senior risk management officer. Crafted with expert knowledge TestGorilla’s tests are created by subject matter experts. We assess potential subject-matter experts based on their knowledge, ability, and reputation. Before being published, each test is peer-reviewed by another expert, then calibrated using hundreds of test takers with relevant experience in the subject. Our feedback mechanisms and unique algorithms allow our subject-matter experts to constantly improve their tests. What our customers are saying TestGorilla helps me to assess engineers rapidly. Creating assessments for different positions is easy due to pre-existing templates. You can create an assessment in less than 2 minutes. The interface is intuitive and it’s easy to visualize results per assessment. VP of engineering, mid-market (51-1000 FTE) Any tool can have functions—bells and whistles. Not every tool comes armed with staff passionate about making the user experience positive. The TestGorilla team only offers useful insights to user challenges, they engage in conversation. For instance, I recently asked a question about a Python test I intended to implement. 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