Question

A: What is the amount of the payments that Henry Winslow must make at the end of each of 8 years to accumulate a fund of $86,200 by the end of the 8th year, if the fund earns 8% interest, compounded annually?

B: Morgan Hitchcock is 39 years old today and he wishes to accumulate $513,000 by his 63rd birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his 39th through his 62th birthdays. What annual deposit must Morgan make if the fund will earn 10% interest compounded annually?

C:Stacy Ross has $20,100 to invest today at 10% to pay a debt of $57,348. How many years will it take her to accumulate enough to liquidate the debt?

D:

Julia Houston has a $28,400 debt that she wishes to repay 4 years from today; she has $19,398 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?

Answer 1

Ans) A)For finding the yearly annual payments, we need to use the formula for Future Value of Annuity-

Formula;

FV of Annuity = P[ { (1+r)^n - 1 } / r ]

Here, P= Periodic Payment , R = Rate of Interest , N = Number of Periods

Therefore by putting the values;

86,200 = P [ { (1+.08)^8 1 } / .08 }

86,200 = P * 10.62

P = 86,200 / 10.62 = 8097.92

Payment made at the end of the year is 8097.92

B) By using the same Future Value of Annuity Formula-

FV of Annuity = P[ { (1+r)^n - 1 } / r ]

Future Value (FV) = $513,000

No of Periods (n) = 22 (from 32nd till 62nd)

Rate = 10%

Therefore putting the value;

513,000 = P [ { (1+.10)^22 - 1) } / .10 ]

513,000 = P * 71.4

P = 7184.87

Annual deposit is 7184.87

C) By using the same Future Value of Annuity Formula-

FV of Annuity = P[ { (1+r)^n - 1 } / r ]

Future Value = 57348

Periodic Payments = 20100

Rate = 10%

Therefore putting the value;

57348 = 20100 [ { (1+.10)^n - 1}/.10]

2.853 = [ { (1+.10)^n - 1}/.10]

n = 35

No of years taken is 35

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