investments and her borrowing power.
4. What would be the value of Karen’s $15,000 in three years if it earned an annual interest rate of 7
percent?
The value of Karen’s $15,000 in three years at an annual interest rate of 7 percent would be $18,375
according to the time value of money table Exhibit A-1 in Appendix A (15,000 x 1.225).
5. Conduct a Web search to obtain information that Karen may find useful. Recommend a Web site that
they might consult when making financial planning decisions.
Student answers will vary. Some possibilities are www.cafp.org and www.canadianfinance.com.
FINANCIAL PLANNING PROBLEMS
(Note: Some of these problems require the use of the time value of money tables in Appendix 1B)
1. Ben Collins plans to buy a house for $65,000. If that real estate property is expected to increase in
value by 5 percent each year, what will its approximate value be seven years from now?
$65,000 1.407 = $91,455
2. Using the rule of 72, approximate the following amounts:
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Instructor’s Manual for Kapoor et al. Personal Finance 7CE.
a. If land in an area is increasing 6 percent a year, how long will it take for property values to
double?
About 12 years (72 / 6)
b. If you earn 10 percent on your investments, how long will it take for your money to double?
About 7.2 years (72 / 10)
c. At an annual interest rate of 5 percent, how long will it take for your savings to double?
About 14.4 years (72 / 5)
3. In 1998, selected automobiles had an average cost of $12,000. The average cost of those same motor
vehicles 10 years later is $16,000. What was the rate of increase for these items between the two time
periods?
($16,000 - $12,000) / $12,000 = .3333 (33.33 percent)
4. How much should you deposit today to have $7,000 in five years if your investment earns a rate of
3% per annum?
7000/(1.03) 5 = $6,038.26
5. The Benevolent Company has agreed to lend you funds to complete the last year of your degree. The
Company will lend you $2,400 today, if you agree to repay a lump sum of $4,000 four years from
now. What is the approximate annual rate of interest that Benevolent is charging you? (Obj. 3)
$2400 = 4000 (DF i%, 4);
Solution: I% = 14%
6. How long will it take to double your money with a growth rate of 5 percent and 12 percent
respectively? (Obj. 3)
15 = 14.4 Years.
2) 72/12 = 6 Years.
7. You discover $40,000 under your pillow, which can be invested at a rate of 18% per year. If you
spend $11,435 per year, how long will the money last? (Obj. 3)
$40,000 = $11,435 (PVAF 18%, n)
or $40,000 = $11,435 x ((1-1/1.18 n )/.18) and solve for n
Solution n= 6 years.
8. What annual payment would be required to pay off a four year, $20,000 loan if the interest rate being
charged is 7%? (Obj. 3)
Payments = [$20,000 / (PVAF 4, 7%)] = $20,000 / 3.387 = $5905
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9. You have $100,000 to purchase a 20-year annuity at 5 percent. What will be the annual payment
from the annuity?
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$100,000 = Payment x PVA factor (Exhibit 1B-4) and Payment = $100,000 ÷ 12.462 = $8,024.
10. Using time value of money tables, calculate the following:
a. The future value of $450 six years from now at 7 percent.
$450 1.501 = $675.45
b. The future value of $800 saved each year for 10 years at 8 percent.
$800 14.487 = $11,589.60
c. The amount that a person would have to deposit today (present value) at a 6 percent interest rate
in order to have $1,000 five years from now.
$1,000 .747 = $747
d. The amount that a person would have to deposit today in order to be able to take out $500 a year
for 10 years from an account earning 8 percent.
$500 6.710 = $3,355
11. Elaine Romberg prepares her own income tax return each year. A tax preparer would charge her $60
for this service. Over a period of 10 years, how much does Elaine save from preparing her own tax
return (assume that she earns 6 percent on a savings account)?
$60 13.181 = $790.86
12. You have $800 in a savings account which earns 6% interest compounded annually. How much
additional interest would you earn in 2 years if you moved the $800 to an account which earns 6%
compounded semi-annually?
Annual compounding $800 (1.06) 2 = $898.88
Semi-annual compounding $800 (1 + .06/2) 2X2 = $900.41 Difference = $1.53
13. What is the future value of $20,000 received in 10 years if it is invested at 6% compounded
annually for the next six years and at 5% compounded annually for the remaining four years?