financing & business planning math quiz quizlet

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.

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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

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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

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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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Answer: 1 2 x \frac{1}{2\sqrt{x}} 2 x ​ 1 ​ .

Step 1: Identify the function for which the derivative is to be found, which is f ( x ) = x f(x) = \sqrt{x} f ( x ) = x ​ .

Step 2: Rewrite the function using exponent notation: f ( x ) = x 1 / 2 f(x) = x^{1/2} f ( x ) = x 1/2 .

Step 3: Apply the power rule for differentiation: f ′ ( x ) = 1 2 x − 1 / 2 f'(x) = \frac{1}{2}x^{-1/2} f ′ ( x ) = 2 1 ​ x − 1/2 .

Step 4: Simplify the derivative: f ′ ( x ) = 1 2 x f'(x) = \frac{1}{2\sqrt{x}} f ′ ( x ) = 2 x ​ 1 ​ .

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20 Business Plan Quiz Questions and Answers

A business plan is a comprehensive document that outlines the goals, strategies, and financial projections of a business venture. It serves as a roadmap for entrepreneurs and stakeholders to understand the direction and viability of the business. Here’s an overview of the key components typically included in a business plan:

Executive Summary: This section provides a concise overview of the entire business plan. It highlights the company’s mission, vision, key objectives, and a summary of the proposed business model.

Company Description: Here, you’ll provide a detailed explanation of your business concept. Include the type of business, its legal structure, location, target market, and any unique selling propositions that set your business apart.

Market Analysis: Conduct thorough market research to understand your industry, target market, and competitors. Identify trends, potential opportunities, and challenges. Explain how your product or service will meet the needs of your target audience better than existing solutions.

Organization and Management: Describe the organizational structure of your business, including key team members, their roles, and relevant experience. Investors want to know that you have a capable team driving the venture.

Article overview

Part 1: 30 business plan quiz questions & answers.

1. Question: What is the primary purpose of a business plan? a) Secure funding b) Improve employee morale c) Enhance customer service d) Increase market competition Answer: a) Secure funding

2. Question: Which section of a business plan outlines the company’s mission and vision? a) Marketing strategy b) Financial projections c) Executive summary d) Company overview Answer: d) Company overview

3. Question: Which of the following is NOT a common business plan component? a) Competitive analysis b) SWOT analysis c) Cash flow statement d) Social media strategy Answer: d) Social media strategy

4. Question: What is the purpose of conducting a market analysis in a business plan? a) Determine the company’s competitors b) Develop financial projections c) Define the company’s mission d) Set employee goals Answer: a) Determine the company’s competitors

5. Question: Which section of a business plan highlights the company’s unique selling proposition (USP)? a) Marketing strategy b) Company description c) Competitive analysis d) Financial projections Answer: a) Marketing strategy

6. Question: What financial document shows a company’s revenues and expenses over a specific period? a) Balance sheet b) Cash flow statement c) Income statement d) Profit and loss statement Answer: c) Income statement

7. Question: In a business plan, what does ROI stand for? a) Return on Investment b) Revenue on Investment c) Risk of Inflation d) Rate of Interest Answer: a) Return on Investment

8. Question: Which business plan section outlines the marketing tactics to promote a product or service? a) Financial projections b) Market analysis c) Marketing strategy d) Company overview Answer: c) Marketing strategy

9. Question: What is a break-even analysis used for in a business plan? a) Identifying potential customers b) Calculating potential profits c) Determining the point of profitability d) Analyzing competitor strategies Answer: c) Determining the point of profitability

10. Question: In a business plan, what does the term “SWOT” stand for? a) Strengths, Weaknesses, Opportunities, Threats b) Sales, Workforce, Objectives, Technology c) Strategies, Workflow, Operations, Targets d) Success, Wealth, Objectives, Tactics Answer: a) Strengths, Weaknesses, Opportunities, Threats

11. Question: What is the purpose of an executive summary in a business plan? a) Provide an overview of the company’s history b) Detail the company’s long-term objectives c) Summarize the key points of the entire plan d) Highlight the company’s competitive advantages Answer: c) Summarize the key points of the entire plan

12. Question: Which financing option involves giving up ownership shares of a company in exchange for capital? a) Debt financing b) Equity financing c) Venture capital d) Angel investing Answer: b) Equity financing

13. Question: What does the term “KPI” mean in a business context? a) Key Performance Indicator b) Key Profit Increment c) Key Planning and Implementation d) Key Personnel Improvement Answer: a) Key Performance Indicator

14. Question: What section of a business plan should discuss the company’s organizational structure and management team? a) Market analysis b) Financial projections c) Company overview d) Marketing strategy Answer: c) Company overview

15. Question: What type of business plan primarily targets internal decision-making and planning? a) Startup business plan b) Strategic business plan c) Operational business plan d) Feasibility business plan Answer: c) Operational business plan

Part 2: Download business plan questions & answers for free

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16. Question: What external factor analysis tool helps identify the political, economic, social, and technological influences on a business? a) PEST analysis b) SWOT analysis c) BCG matrix d) Porter’s Five Forces Answer: a) PEST analysis

17. Question: Which statement best describes a vision statement in a business plan? a) Outlines the short-term goals of the company b) Identifies potential risks and challenges c) Describes the company’s future aspirations d) Analyzes the company’s target market Answer: c) Describes the company’s future aspirations

18. Question: What is the purpose of conducting a competitive analysis in a business plan? a) Identify potential partners b) Analyze customer feedback c) Evaluate strengths and weaknesses of competitors d) Forecast financial performance Answer: c) Evaluate strengths and weaknesses of competitors

19. Question: Which financing option involves borrowing money that must be repaid with interest over time? a) Debt financing b) Equity financing c) Venture capital d) Angel investing Answer: a) Debt financing

20. Question: What does the term “ROI” stand for in the context of financial analysis? a) Revenue on Investment b) Return on Innovation c) Risk of Inflation d) Return on Investment Answer: d) Return on Investment

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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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Financial Math Quiz

To succeed in life, you have to be good at maths as well as finance. Mathematical finance (a mix of both), also known as quantitative finance, is a field of applied maths, concerned with the mathematical modeling of financial markets. It is one of the rarest yet important skills to have. Take this test to test your knowledge about Financial Math and try to get better at it.

A sum fetched a total simple interest of R4016.25 at a rate of 9% p.a in 5 years.what is the sum?

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A sum of money at simple interest amounts to R815 in 3 years and R854 in 4 years.the sum is:

Mr zwane invested an amount of r13.900 divided in two different schemes a and b at the simple interest rate of 14% p.a and 11% p.a respectively. if the total amount of simple interest earned in 2 years be r3508,what was the amount invested in scheme b , how much time will it take for an amount of rs. 900 to yield rs. 81 as interest at 4.5% per annum of simple interest,  mr. thomas invested an amount of rs. 13,900 divided in two different schemes a and b at the simple interest rate of 14% p.a. and 11% p.a. respectively. if the total amount of simple interest earned in 2 years be rs. 3508, what was the amount invested in scheme b, arun took a loan of rs. 1400 with simple interest for as many years as the rate of interest. if he paid rs.686 as interest at the end of the loan period, what was the rate of interest, which of these is not a deduction from your pay each month.

Direct Debit

National Insurance

Sean earns £6.83 per hour parking cars at an airport. If he works for 38 hours per week, how much is his weekly gross pay?

£190.25

£315.12

£255.45

Charlie earns £1,980 per month as a consumer reviewer. She pays income tax at a rate of 20%. How much tax does Charlie pay per month?

£1584

£1122

Work out the total amount in your bank if £250 is invested and earns simple interest of 2% for 2 years.

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