Question

Using the appropriate interest table, provide the solution to each of the following four questions by computing the unknowns. Click here to view factor tables What is the amount of the payments that Tony Winslow must make at the end of each of 9 years to accumulate a fund of $97,700 by the end of the 9th year, if the fund earns 9% interest, compounded annually? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.) Payment at the end of each year $ Chris Hitchcock is 40 years old today and he wishes to accumulate $490,000 by his 64th birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his 40th through his 63th birthdays. What annual deposit must Chris make if the fund will earn 12% interest compounded annually? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.) Annual deposit $ Sally Ross has $18,700 to invest today at 11% to pay a debt of $58,938. How many years will it take her to accumulate enough to liquidate the debt? (Round answer to 0 decimal places, e.g. 45.) years Candice Houston has a $25,600 debt that she wishes to repay 5 years from today; she has $15,192 that she intends to invest for the 5 years. What rate of interest will she need to earn annually in order to accumulate enough to pay the debt? (Round answer to 0 decimal places, e.g. 7%.) Rate of interest %

Answer 1

Solution 1:

Required fund after 9 years = $97,700

Let investment amount at the end of each year = a

a = Required fund / Compound amount factor for ordinary annuity 9% for 9 years

= $97,700 / 13.02104 = $7,503

Solution 2:

Required fund after 24 years = $490,000

Let investment amount at the beginning of each year = a

a = Required fund / Compound amount factor for annuity due at 12% for 24 periods

= $490,000 / 132.33387 = $3,703

Solution 3:

Amount of investment= $18,700

Requried future value to pay off debt = $58,938

Rate of interest = 11%

Let time taken to accumulate $58,938 is t years

Now P * (1+r)^t = $58,938

$18,700 (1 + 0.11) ^ t = $58,938

t = 11 years

Solution 4:

Amount of investment= $15,192

Requried future value to pay off debt = $25,600

Required time = 5 years

Let desired rate of interest is r to accumulate $25,600 in 5 years

Now P * (1+r)^t = $25,600

$15192 (1 + r) ^ 5 = $25,600

r = 11%