Question 1

Kent sold his car to Carolynn for $2000 down and monthly payments of $259.50 for 3½ years, including interest at 7.5% compounded annually. What was the selling price of the car?

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Question 2

LeVero's monthly payments of $567.89 will pay off his mortgage loan in 4 years and 7 months. The interest rate on his mortgage is 6.6% compounded semiannully. What is the current balance on the loan?

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Question 3

Advantage of Early Investing Go to the Student Edition on this student textbook's OLC. In the navigation bar, select "Chapter 10" in the drop-down box. In the list of resources for Chapter 10, select "Links in Student textbook" and then click on the link named "Early Investing." When the Web page loads, scroll down the screen to find the link named "Advantage of Early Investing." Click on it. The window that opens allows you to enter data to compare three investment plans. For each plan, enter your regular end-of period investment contribution, the frequency of contribution, the age range over which you will contribute, any initial amount already accumulated, and the projected rate of return. Compare the outcomes at age 65 for the following three alternatives:
(i) Plan A: Invest $100/month starting at age 25.
(ii) Plan B: Invest $200/month starting at age 35.
(iii) Plan C: Invest $400/month starting at age 45.
Enter 9% for the growth rate. The calculations will assume annual compounding. After completing the data entry, click on "Submit." A new window opens presenting a table of future values at various ages for each investment plan. Scroll down the window to view an attractive graphic comparing the growth of the three plans.
a) Calculate the total of the nominal contributions under each plan. Compare them using a ratio A:B:C with terms reduced to small integers.
b) Compare the future values at age 65 in a ratio A:B:C. Reduce the ratio so that the smallest term is "1."

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Question 4

How much larger will the value of an RRSP be at the end of 25 years if the contributor makes month-end contributions of $300 instead of year-end contributions of $3600? In both cases the RRSP earns 8.5% compounded semiannually.

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Question 5

Year-end contributions of $1000 will be made to a TFSA for 25 years. What will be the future value of the account if it earns 7½ % compounded monthly for the first 10 years and 8% compounded semiannually thereafter?

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Question 6

Gloria has just made her ninth annual $2000 contribution to her TFSA. She now plans to make semiannual contributions of $2000. The first contribution will be made six months from now. How much will she have in her TFSA 15 years from now if the plan has earned and will continue to earn 8% compounded quarterly?

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Question 7

The Toronto Raptors announce the signing of their top draft pick to a "7-year deal worth $43.2 million." The player will earn $200,000 at the end of each month for the first three years, and $600,000 at the end of each month for the subsequent four years. How do the Raptors get the $43.2 million figure? To the nearest $1000, what is the current economic value of the deal if money can earn 7% compounded annually?

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Question 8

What is the current economic value of an inheritance that will pay $2000 to the beneficiary at the beginning of every three months for 20 years, starting when the beneficiary reaches 20 years of age, 4½ years from now? Assume that money is worth 6% compounded monthly. (Round to the nearest dollar.)

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Question 9

Sabrina borrowed $30,000 at an interest rate of 7% compounded quarterly. Monthly payments of $356.83 will commence after a period of deferral and will pay off the loan over the subsequent 12½ years. What is the length of the period of deferral?

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Question 10

An investor purchased a deferred annuity contract for $4608.07, a price calculated to provide a rate of return on investment of 9.75% compounded monthly. The semiannual payments of $400, once started, continue for a term of 15 years. How long is the period of deferral?

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Question 11

What amount of money invested now will provide payments of $500 at the end of every month for five years following a four-year period of deferral? The money will earn 7.2% compounded monthly.

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Question 12

Calculate the future value of an ordinary annuity consisting of monthly payments of $300 for five years. The rate of interest was 9% compounded monthly for the first two years and will be 7.5% compounded monthly for the last three years.

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Question 13

How much larger will the value of an RRSP be at the end of 20 years if the contributor makes month-end contributions of $500 instead of year-end contributions of $6000? In both cases the RRSP earns 7.5% compounded semiannually.

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Question 14

A Province of Ontario bond has 14½ years remaining until it matures. The bond pays $231.25 interest at the end of every six months. At maturity, the bond repays its $5000 face value in addition to the final interest payment. What is the fair market value of the bond if similar provincial bonds are currently providing investors with a return of 7.8% compounded semiannually?

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Question 15

Calculate the future value of investments consisting of payments of $800 at the end of each calendar quarter for seven years. The rate of interest earned will be 10% compounded quarterly for the first 30 months and 9% compounded semiannually for the remainder of the annuity's term.

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Question 16

A mortgage broker offers to sell you a mortgage loan contract that will pay $900 per month for the next 2¾ years. At that point, the principal balance of $37,886 is due and payable. What should you pay for the contract if you require a return of 7.2% compounded monthly?

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Question 17

Suppose Evan contributes $2000 to his RRSP at the end of every quarter for the next 15 years and then contributes $1000 at each month's end for the subsequent 10 years. How much will he have in his RRSP at the end of the 25 years? Assume that the RRSP earns 8% compounded semiannually.

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Question 18

Surinder is saving $50 per month. How much will she have in her account in five years if her account is earning 3.5% compounded monthly?

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Question 19

Sam invests $5000 per year in an RRSP. What will be the value of the plan after 30 years if interest is 4.5% compounded annually. How much interest did Sam's investment earn?

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Question 20

Saminder quit smoking and saves $80 per month previously spent on cigarettes. He invests the money at 5% compounded monthly. How much will he have in 10 years?

Accepted Answer

The future value of a series of monthly investments can be calculated using the future value of an annuity formula: FV = P * [(1 + r)^nt - 1] / r, where P is the monthly investment ($80), r is the monthly interest rate (5% annual rate / 12 months = 0.0041667), n is the number of times the interest is compounded per year (12), and t is the number of years (10). Plugging in these values gives the future value closest to $12,422.58.

Quiz 10: Ordinary Annuities: Future Value and Present Value