206 Chapter 4 Annuities
- Aaron would like to have $2,000,000 when he retires 42 years from now. How much should he set aside each week if
his investments can earn 9.1%? - McCabe Industrial Corp. borrowed $750,000 for an upgrade of its plant, borrowing the money at 8.5% compounded
daily for 5 years. McCabe is not required to make any payments to the lender until maturity, but is required to set up a
sinking fund for the purpose of accumulating the loan’s maturity value. If they make quarterly deposits into an account
earning 4.8%, how much should each payment be? - Dawn deposited $3,000 into an investment account paying 5.29% compounded daily for 5 years. How much total
interest will she earn? - I have a $3,031.59 balance on my credit card. The interest rate is 21.95%. If I pay $300 this month, how much of
my payment will go toward interest? What will my balance be after my payment (assuming I make no additional
charges). - Nicole is about to retire, and has $800,000 saved in a 401(k) plan, from which she wants to take monthly
payments for the next 25 years. If the account can be expected to earn 6% interest, how much will each monthly
payment be? - Mary just won the Rhode Island Lottery, with a total jackpot of $5,200,000. She will receive the money spread out as
equal payments at the beginning of each year for the next 26 years. The $5,200,000 is the total of all payments, not
the present value. So she is entitled to 26 annual payments of $5,200,000/26 $200,000 per year. If she decided
instead to take her winnings as one lump sum, the interest rate used would be 6%. How much would she receive as a
lump sum? (Do not take taxes into account in this calculation.) - Harald put $2,000 into his retirement savings account at the end of each year for 40 years. The account earned an
interest rate of 7.2%.
a) How much did his account grow to at the end of the 40 years?
b) Suppose that Harald decides to use the money in his account to provide a monthly income in retirement. If his
account earns 5.4% during his retirement, how much can he withdraw each month if he wants his account to last
20 years?
- Find the future value of $25 a week for 30 years at 7.23%.
- Walt borrowed $30,000 for 7 years at 8.4%. Find his monthly payment, and construct an amortization table for his fi rst
three payments.
Month Payment Interest Principal
Remaining
Balance
1
2
3