Question

3 Years ago Jake borrowed R7500 from Martha. The condition was that he would pay her back im 7 years' time at an interest rate of 11.21% per year, compounded semi aunally. 6 Months ago he also borrowed R25000 from Martha at 9.45% per yar compounded monthly. Jake would like to pay off his debt in 4 years from now

(a) what is the amount that Jake will have to pay Martha 4 years from now?

(b) after seeing shat he must pay Martha, Jake decides to reschedule his debtas 2 equal payments: one mou and one 3 years from now. Martha agrees on condition that the new agreement that will run from now will be subjected to 10.67% interest, compounded quaterly. What is the amount Jake will pay Matha 3 years from now?

Answer 1

a) For the first loan, there are 7 x 2 = 14 semi-annual periods of compounding.

FV = PV x (1 + r)^n = 7,500 x (1 + 11.21%/2)^14 = $16,093.26

There are total 54 months after which Jake will pay Martha.

FV = PV x (1 + r)^n = 25,000 x (1 + 9.45%/12)^54 = $38,185.66

Total amount Jake would pay Martha = $54,278.92

b) The value of first debt today = 7,500 x (1 + 11.21%/2)^6 = $10,403.23

The value of second debt today = 25,000 x (1 + 9.45%/12)^6 = $26,204.75

Total value of debt today = $36,607.98

Assume that the value of payment = X then

$36,607.98 = X + X / (1 + 10.67%/4)^12

=> X = $21,171.35 should be payment.