Chapter 5 Time Value of Money

Question 1.

Using the appropriate interest table, provide the solution to each of the following four questions by computing the unknowns. (Round factor values to 4 decimal places, e.g., 1.2345 and final answers to 0 decimal places, e.g., 54,321.)

(a) What is the amount of the payments that Ned Winslow must make at the end of each of 8 years to accumulate a fund of $90,000 by the end of the eighth year, if the fund earns 8% interest, compounded annually?

(b) Diane Ross has $20,000 to invest today at 9% to pay a debt of $47,347. How many years will it take her to accumulate enough to liquidate the debt?

(c) Robert Hitchcock is 40 years old today and he wishes to accumulate $500,000 by his sixty-fifth birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his fortieth through his sixty-fourth birthdays. What annual deposit must Robert make if the fund will earn 8% interest compounded annually?

(d) Cindy Houston has a $27,600 debt that she wishes to repay 4 years from today; she has $19,553 that she intends to invest for the 4 years. What rate of interest will she need to earn annually in order to accumulate enough to pay the debt?

Question 2.

Howie Long has just learned he has won a $500,000 prize in the lottery. The lottery has given him two options for receiving the payments. (1) If Howie takes all the money today, the state and federal governments will deduct taxes at a rate of 46% immediately. (2) Alternatively, the lottery offers Howie a payout of 20 equal payments of $36,000 with the first payment occurring when Howie turns in the winning ticket. Howie will be taxed on each of these payments at a rate of 25%.

Assuming Howie can earn an 8% rate of return (compounded annually) on any money invested during this period, which payout option should he choose?

(1) Lump sum alternative:

(2) Annuity alternative: (round to nearest dollar)

(3) Which payout option should he choose?