Present & Future Values:
Annuities & Perpetuities
Chapter
Six
Problem Set – Present & Future
Values: Annuities & Perpetuities
1.
2.
3.
4.
A good friend has offered to let you purchase a new investment instrument.
The deal is you pay $5,000 today. In return, he will give you back
payments of $1,000 one year from today, $2,000 two years from today and
$3,000 three years from today. If your opportunity cost of capital is 10%,
should you accept the deal? (Reject – NPV is -$184.07)
You currently have $2,500 on deposit at your local bank. You intend to
make deposits of $1,000 one year from today, $2,500 two years from today
and $4,000 four years from today. How much will you have five years from
today, given that you are earning 4%? ($11,183.66)
You intend to save $1,000 per year for five years, beginning immediately.
If you can earn 6%, how much will you have on deposit 8 years from
today? ($7,116.70)
You began contributing $1,000 per year to an RRSP. You intend to
continue this pattern for the next 30 years. If you are earning 6%,
compounded annually, how much will you have at the end of the 30 years?
($79,058.19)
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Problem Set – Present & Future
Values: Annuities & Perpetuities
5.
6.
7.
8.
9.
GMC is currently offering car loans at 1% interest per month. If the car
you want costs $30,000 and you intend to repay the loan over 6 years,
how much are your monthly payments? ($586.51)
Winners of a recent couples version of “Fear Factor” were told that they
would win $1,000,000. However, what they really won was $25,000 per
year paid annually for 40 years. If an appropriate discount rate is 10%,
what is the present value of their winnings? ($244,476.27)
You have invested $5,000 in a security which will pay you $1,000 per year
for 7 years. What is your annually compounded rate of return? (9.20%)
You borrowed $20,000 from your parents to help fund your education. If
you can afford to make payments of $250 per month and they are charging
interest of 6%, compounded monthly, how many months will it take to pay
off the loan? (102.4 months)
You have decided to lease a new car, rather than purchase it. If the lease
payments are $300 per month for 48 months, paid at the start of each
month, what is the present value of the lease, given a discount rate of 7%?
($12,601.14)
3
Problem Set – Present & Future
Values: Annuities & Perpetuities
10. A consol bond pays a fixed coupon forever. If you can
purchase a $1,000 consol bond paying a 4% coupon
when market interest rates are 6%, how much would
you expect to pay for the bond? ($666.67)
11. You have made your fortune and decided to fund a
scholarship for worthy finance students at the University
of Lethbridge. You want the scholarship to start at
$2,500 per year and grow at 3% per year, to offset
inflation. If interest rates are currently 7%, how much
money must you contribute today to fund the
scholarship? ($62,500)
4
Problem Set – Present & Future
Values: Annuities & Perpetuities
10. Natural gas has just been discovered on your parent’s
farm. If the well is expected to produce royalties of
$50,000 in year one and then decrease by 5% annually
forever, how much would you sell your interest for, if you
use a discount rate of 10%? ($333,333.33)
11. TransAlta is expected to pay a dividend of $1.00 per
share at the end of the year. If the dividend is then
expected to grow at 5% per year, how much would you
pay for one share of TransAlta, given that you require a
return of 12%? ($14.29)
5
Problem Set – Present & Future
Values: Annuities & Perpetuities
12. You want to retire with $2,000,000 of liquid assets in 40
years. If you can earn 8% compounded monthly, how
much should you save every month to meet your goals?
($572.90)
13. Jill intends to save $4,000 per year for the next ten
years. At the end of ten years, she is going to purchase
a BMW for $50,000. She will then save money for the
next 25 years, at which time she will retire. During her
30 years of retirement, she wants a yearly income of
$45,000. If she can earn 7% on her money, how much
does Jill need to save every year during the 25 years
prior to her retirement? ($8,376.84)
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Problem Set – Present & Future
Values: Annuities & Perpetuities
14. Bank A is offering GICs at 6%, compounded quarterly. Bank B is
offering GICs at 5.85% compounded monthly. Which bank is
offering the highest effective annual interest rate? (Bank A –
6.14%; Bank B – 6.01%)
15. If the effective annual interest rate is 10%, compounded monthly,
what is the nominal rate? (9.57%)
16. You want to obtain a $100,000 Canadian residential mortgage. If
the bank is currently offering mortgages at 6%, compounded semiannually and repaid monthly over 25 years, how much are your
monthly payments? ($639.81)
17. How much are the total interest payments on the mortgage in
Question 16? ($91,941.99)
18. If you shorten the term of the mortgage in Question 16 to 15 years,
what happens to your monthly payments? What about the total
amount of interest paid over the life of the loan? ($839.88;
$51,178.90)
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