Question

# E6.16 (LO 3) (Retirement of Debt) Ricky Fowler borrowed \$70,000 on March 1, 2018. This amount...

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

 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)