1.

You deposit $5,000 in an account that earns 12% compounded annually. Compute the
account balance at the end of:
a.
b.
c.

1 year
20 years
40 years

FUTURE VALUE

2.

You deposit $100,000 in an account that earns a 10% annual rate of return. You have
decided that at the end of each year you will withdraw the interest that is credited to your
account. If you plan on closing the account at the end of the tenth year, how much are you
able to withdraw at that point in time?

FUTURE VALUE, EFFECTIVE RATE CALCULATION IS REQUIRED

3.

You have the opportunity to deposit $10,000 into one of two accounts. The Optimum
account offers to pay 12% compounded annually while the prime account offers to pay 12%
compounded monthly. If you plan on leaving the money in the account for 10 years, what
will be the difference between the Optimum and Prime account balances at the end of the
tenth year?

PRESENT VALUE

4.

If you expect to inherit $50,000 at the end of the 20 years, compute the present value of the
inheritance at the following annual interest rates.
a.
b.
c.

6%
12%
24%

5-1

Name:___________________________FIN3087
Date:_________________
PRESENT VALUE

5.

If you require a 10% rate of return on the following investment opportunities, which would
you prefer–$100,000 today, $250,000 ten years from today, or $12,000 per year at the end
of each of the next 20 years?

PRESENT VALUE, EFFECTIVE RATE CALCULATION IS REQUIRED

6.

Mirage Investments is offering a investment opportunity that pays a 10% annual rate of
return, compounded quarterly. How much would you have to pay for this investment if
Mirage has agreed to pay you $32,000 at the beginning of the sixth year?

DETERMINATION OF THE NUMBER OF TIME PERIODS

7.

How long will it take to double your initial deposit into an Escalator Account, if the bank
offering the account pays the following interest rates:
a.
b.
c.

9% compounded annually
14% compounded annually
9% compounded monthly

DETERMINATION OF THE NUMBER OF TIME PERIODS

8.

Insolvent Savings and Loan has advertised an account that pays 8% compounded annually.
In the ad, Insolvent provides a example of a hypothetical account. The ad shows that a
customer depositing $10,000 with the bank can achieve an account balance of $100,627.
Due to a misprint, it is not clear from the ad how long a customer would have to leave the
money in the account.
It is up to you to correct that misprint–how long does this
hypothetical customer have to leave the money in the account?

INTEREST RATE DETERMINATION

9.

Compute the effective annual interest rate paid by your bank if your initial deposit with the
bank doubles in:
a.
b.
c.

5 years
10 years
20 years

5-2

Name:___________________________FIN3087
Date:_________________
INTEREST RATE DETERMINATION

10. Over a 13 year time period, your $3,000 investment in gold coins has increased in value to
$15,000. What effective annual rate of return have you earned on your investment in gold?
What is your holding period return on this investment?
PRESENT VALUE OF AN ANNUITY

11. Mutual Benefit is offering a "Ultimate Opportunity" annuity contract that offers investors a
14% annual rate of return. The contract specifies that Mutual Benefit will pay the investor
an equal amount at the end of each contract year. You have decided to buy a contract that
provides an annual payment of $10,000 per year at the end of each of the next 20 years.
How much are you going to have to pay Mutual Benefit for this annuity contract?
PRESENT VALUE OF AN ANNUITY

12. You just lost a lawsuit which requires you to pay the plaintiff $500,000. The judge, not
being well versed in finance, has agreed to your request that you be allowed to pay $25,000
per year at the end of each of the next 20 years.
a.
b.
c.

If you can invest in government securities that compound interest at an annual rate of
7%, how much do you have to set aside today in order to insure that the payments are
made to the plaintiff?
If your broker tells you that by investing in securities issued by corporations you can
earn a compound annual rate of 12%, how much do you have to set aside today in order
to insure that the payments are made to the plaintiff?
Which investment alternative would you select? Should the plaintiff care about your
decision?

FUTURE VALUE OF AN ANNUITY

13. You have decided to deposit $1,000 per year at the end of each of the next 15 years in an
account that earns 5% compounded annually. What is the account balance at the end of the
fifteenth year?
FUTURE VALUE OF AN ANNUITY

14. Since the big promotion and the raise that goes with it finally came through, you have
decided to get serious about saving some money. You are going to save $5,000 per year at
the end of each of the next 25 years, but are unsure where to invest the money. If you invest
the money in certificates of deposit, you forecast that you will earn a 7.5% effective annual
rate of return. An alternative is to invest the money in a High Yield bond fund. The fund
claims that last year it generated a 14% effective annual rate of return, but notes that past
performance may not reflect future returns.

5-3

Name:___________________________FIN3087
Date:_________________
a. Compute the account balance at the end of the twenty-fifth year if you select the
certificate of deposit investment alternative.
b. Compute the account balance at the end of the twenty-fifth year if you select the High
Yield investment alternative. Assume that the fund earns a 14% annual return.
c. Given the difference in the account balances, why would anyone purchase certificates
of deposit?

PRESENT VALUE OF ANNUITY DUE

15. Three years ago you borrowed $30,000 in order to purchase a boat. The lender agreed to a 7
year loan at a 14% annual interest rate. A unique feature of the loan is the requirement that
the annual payment of $6,136.64 be made at the beginning of each year. It is the end of the
third year and you are about to write a check for the fourth payment. Since this last year
was fairly prosperous you have decided to pay off the entire loan balance at this time. How
much do you have to pay in order to repay the entire remaining balance on the loan?
FUTURE VALUE OF AN ANNUITY DUE

16. You have decided to deposit $1,500 per year at the beginning of each of the next 10 years in
an account that earns 8% compounded annually. What is the account balance at the end of
the tenth year?