Question

E6.16 (LO 3) (Retirement of Debt)

Ricky Fowler borrowed $70,000 on March 1, 2018. This amount plus accrued interest at 6% compounded semiannually is to be repaid March 1, 2028. To retire this debt, Ricky plans to contribute to a debt retirement fund five equal amounts starting on March 1, 2023, and for the next 4 years. The fund is expected to earn 5% per annum.

Instructions

How much must be contributed each year by Ricky Fowler to provide a fund sufficient to retire the debt on March 1, 2028?

please give a explanation this two steps

The Future value of an annuity due of 1 for 5 period

(FVAD) FV of annuity = FV ordinary annuity *factor

                         = 5,525,63 * (1+0,05)

                         = 5,8019

Periodic Rent ($126,428 ÷ 5,8019*) = 21,791

Answer 1

Future value of $ 70000 at 6% p.a., ie.6%/2=3% interest compounded semi-annually for 10 yrs.*2=20 semi-annual periods =

Future value=Present value of loan*(1+interest rate)^ No.of compounding periods

ie. 70000*(1+0.03)^20=

126428

OR using FV of $1 factor for 20 periods , for r= 3%----1.80611

70000*1.80611=

126428

The above sum(126428) is the future value of the total debt retirement funds

which is 5 beginning-of -the year annuities

at 5% p.a.

So, we use Future Value of annuity due(beginning -of-yr.payments)

which is FV of ordinary annuity factor*(1+r)

ie.FVOA factor for i=5% & n= 5 is 5.52563

so, FVADue factor= 5.52563*1.05= 5.8019

Now, FVADue=Pmt.*(FVADue Factor)

ie.126428=Beg.of yr. pmt*5.8019

so, that beg. Of yr. pmt.=126428/5.8019=

21791

(Answer)