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Bongani, the manager of a construction company is renovating a home and has expenses of R200 000.00 now and another R41 812.00 in six months' time. As he finds it difficult to find the cash now, he proposes to settle all the debt after six months with a single payment. The debt is subject to an interest rate of 9.5% per annum, compounded quarterly. What is the value of the payment that will settle his debt at the end of month six?

Answer :

The value of the payment that will settle the debt at the end of month six is R251,424.81

Which amount of debt needs to be compounded forward?

The only amount of debt which needs to be compounded forward , I mean that its future equivalent amount needs to be determined is the debt due now, over a period of 6 months it would earn

FV=PV*(1+r/m)^N

FV=future value of debt due in 6 months=unknown

PV=present value=debt due now=R200 000.00

r=annual interest rate=9.5%

m=number of compounding per year=4(4 quarters in a year)

N=number of quarters that payment needs to be delayed=2(2 quarters=6months)

FV=200,000*(1+9.5%/4)^(2)

FV= R209,612.81

Single payment=FV of debt due now+ amount due in six months

Single payment=209,612.81+41 812.00

single payment=R251,424.81

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