200 Chapter 4 Annuities
B. “Annuities” with an Extra Payment
- Suppose Kerry deposits $2,000 each year into an investment account every year. The only exception to this schedule is
that for her 10th payment she deposits $5,000 instead of her usual $2,000 deposit. If her account earns 6.98%, how
much will she have at the end of 30 years? - Allyson deposits $3,000 at the beginning of each year into an account earning 10% for 25 years, except that in the
15th year she deposits an additional $5,000 above and beyond her usual $3,000 deposit. How much will she have at
the end of the 25 years? How much total interest will she earn?
C. “Annuities” with a Missing Payment
- Mike deposited $2,500 into his individual retirement account (IRA) every year for 25 years. He missed his deposit in
the eighth year because he was temporarily laid off, but other than that he has kept his deposits up every year. If his
account earned 7.72%, what was his account value at the end of 25 years? - Suppose you deposit $1,250 each year for 30 years, except that in year 21 you deposit only $750 instead of your usual
$1,250. How much do you have at the end of the 30 years, assuming your account earns 5.25%?
D. “Annuities” with Multiple Missing/Extra Payments
- Suppose that the Cauchy-Schwartz Equalization Corp set aside $150,000 each quarter for 12 years into a special fund
to cover potential environmental cleanup costs. For the next 8 years, the company reduced its deposits to $80,000 per
quarter. Find the value of this account at the end of 20 years, assuming it earned a 5.3% interest rate for the entire
period. - Kelly deposited $135 per month into her retirement account for 20 years. For the next 12 years she increased her
deposits to $175 per month. Assuming she earned 8.13%, fi nd her account’s future value. Find the total interest
earned on this account.
E. “Sinking Funds” That Don’t Start from Scratch
- Bud has $1,357.15 in a special vacation savings account. He hopes to have $2,500 in this account 1 year from now.
If his account earns 6% interest, how much does he need to deposit each month to reach his goal? - The Business Department at McKeanville Community College is trying to raise money for a scholarship fund. The
department’s goal is to have $25,000 in the scholarship fund in 5 years. Right now there is $7,346.19 in the fund.
Assuming that the fund earns 7.15%, and that no scholarships will be paid from this fund until the goal is reached, how
much needs to be deposited to this fund each quarter to reach the goal?
F. Grab Bag
- a. Lucy has $275,935 in her individual retirement account right now. She wants to have $1,500,000 in this account
in 20 years. Assume that her account earns 6.85%. How much does she need to deposit each month to reach
this goal?
b. If she lowers her goal to $750,000 in 20 years, how much does she need to deposit each month to reach this
goal?