1 What is the amount of the payments that Alan Winslow must

1. What is the amount of the payments that Alan Winslow must make at the end of each of 10 years to accumulate a fund of $97,300 by the end of the 10th year, if the fund earns 10% 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 $

2. Adams Hitchcock is 39 years old today and he wishes to accumulate $470,000 by his 62nd 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 61th birthdays. What annual deposit must Adams 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 $

3. Carla Ross has $18,300 to invest today at 11% to pay a debt of $42,173. How many years will it take her to accumulate enough to liquidate the debt? (Round answer to 0 decimal places, e.g. 45.)

_____ years

4. Pearl Houston has a $29,000 debt that she wishes to repay 4 years from today; she has $19,103 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? (Round answer to 0 decimal places, e.g. 7%.)

Rate of interest %

Solution

1) The annual payment at the end of each 10 years will be computed as follows:-

Future Value Factors:

FVF(10%,9 yrs) = 2.35795 (payment at the end of Ist year will remain invested for 9 years)

FVF(10%,8 yrs) = 2.14359 (payment at the end of 2nd year will remain invested for 8 years)

Similarly, FVF(10%,7yrs) = 1.94872, FVF(10%,6 yrs) = 1.77156, FVF(10%,5 yrs) = 1.61051

FVF(10%,4 yrs) = 1.4641, FVF(10%,3 yrs) = 1.331, FVF(10%,2 yrs) = 1.21, FVF(10%,1 yr) = 1.10

FVF(10%,0 yrs) = 1 (payment at the end of 10th year will remain invested for zero year)

FVAF = 2.35795+2.14359+1.94872+1.77156+1.61051+1.4641+1.331+1.21+1.1+1 = 15.93743

Annual Payment*FVAF = $97,300

Annual Payment*15.93743 = $97,300

Annual Payment = $97,300/15.93743 = $6,105 per annum

2) Total time for accumulation is 23 years (62 years - 39 years)

Annual deposit *FVAF(12%,23 yrs) = Desired Accumulated amount

Annual deposit*104.6029 = $470,000

Annual deposit = $470,000/104.6029 = $4,493

3) $18,300*FVF(11%, t yrs) = $42,173

FVF(11%, t yrs) = $42,173/$18,300 = 2.3045

The FVF of 2.3045 @11% is for 8 years in the future value table. Therefore he should accumulate for 8 years to liquidate the debt.

4) Total Interest required to be earned = $29,000-$19,103 = $9,897

Annual interest = $9,897/4 years = $2,474 per year

Rate of interest = Annual interest/Amount invested = ($2,474/$19,103)*100 = 12.95% (i.e. 13% per annum)