# 4 TVM practice problems

```Time Value of Money Worksheet
1.
How much interest is earned in just the third year on a \$1,000 deposit that earns 7% interest
compounded annually?
2.
Assume the total expense for your current year in college equals \$20,000. How much would
your parents have needed to invest 21 years ago in an account paying 8% compounded annually to
cover this amount?
3.
In calculating the present value of \$1,000 to be received 5 years from today, the discount
factor has been calculated to be .7008. What is the apparent interest rate?
4.
What will be the approximate population of the United States, if its current population of
300 million grows at a compound rate of 2% annually for 25 years?
5.
If the future value of an annuity due is \$25,000 and \$24,000 is the future value of an
ordinary annuity that is otherwise similar to the annuity due, what is the implied discount rate?
Time Value of Money Worksheet
6.
You invested \$1,200 three years ago. During the three years, you earned annual rates of
return of 4.8%, 9.2%, and 11.6%. What is the value of this investment today?
7.
You will be receiving cash flows of: \$1,000 today, \$2,000 at end of year 1, \$4,000 at end of
year 3, and \$6,000 at end of year 5. What is the present value of these cash flows at an interest rate
of 7%?
8.
A perpetuity of \$5,000 per year beginning today is said to offer a 15% interest rate. What is
its present value?
9.
A corporation has promised to pay \$1,000 20 years from today for each bond sold now. No
interest will be paid on the bonds during the 20 years, and the bonds are discounted at an interest
rate of 7%, compounded semiannually. Approximately how much should an investor pay for each
bond?
10.
Three thousand dollars is deposited into an account paying 10% annually to provide three
annual withdrawals of \$1,206.34 beginning in one year. How much remains in the account after the
second payment has been withdrawn?
Time Value of Money Worksheet
11.
How many monthly payments remain to be paid on an 8% mortgage with a 30-year
amortization and monthly payments of \$733.76, when the balance reaches one-half of the \$100,000
mortgage?
12.
What is the present value of a four-year annuity of \$100 per year that begins 2 years from
today if the discount rate is 9%?
13.
Your retirement account has a current balance of \$50,000. What interest rate would need to
be earned in order to accumulate a total of \$1,000,000 in 30 years, by adding \$6,000 annually?
14.
Approximately how much should be accumulated by the beginning of retirement to provide
a \$2,500 monthly check that will last for 25 years, during which time the fund will earn 6% interest
with monthly compounding?
15.
On the day you retire you have \$1,000,000 saved. You expect to live another 25 years during
which time you expect to earn 6.19% on your savings while inflation averages 2.5% annually.
Assume you want to spend the same amount each year in real terms and die on the day you spend
your last dime. What real amount will you be able to spend each year?
Time Value of Money Worksheet
16.
What APR is being earned on a deposit of \$5,000 made 10 years ago today if the deposit is
worth \$9,848.21 today? The deposit pays interest semiannually.
17.
Would a depositor prefer an APR of 8% with monthly compounding or an APR of 8.5% with
semiannual compounding?
18.
A credit card account that charges interest at the rate of 1.25% per month would have an
annually compounded rate of _____ and an APR of ____.
19.
A loan officer states, "Thousands of dollars can be saved by switching to a 15-year mortgage
from a 30-year mortgage." Calculate the difference in payments on a 30-year mortgage at 9%
interest versus a 15-year mortgage with 8.5% interest. Both mortgages are for \$100,000 and have
monthly payments. What is the difference in total dollars that will be paid to the lender under each
loan? (Round the monthly payment amounts to 2 decimal places.)
20.
You are considering the purchase of a home that would require a mortgage of \$150,000.
How much more in total interest will you pay if you select a 30-year mortgage at 5.65% rather than a
15-year mortgage at 4.9%? (Round the monthly payment amount to 2 decimal places.)
```
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