The Mathematics of Money

(Darren Dugan) #1

206 Chapter 4 Annuities



  1. 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%?

  2. 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?

  3. Dawn deposited $3,000 into an investment account paying 5.29% compounded daily for 5 years. How much total
    interest will she earn?

  4. 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).

  5. 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?

  6. 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.)

  7. 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?


  1. Find the future value of $25 a week for 30 years at 7.23%.

  2. 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
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