Answer to Question #318336 in Financial Math for Tower

Question

Round of the answer to this question to the nearest rand . David borrowed R911012 to refurbish his holiday home. The loan requires monthly repayment over 12 years . When he borrowed the money the interest rate was 12,4% per annum, compounded monthly but five years later the bank increase the annual interest rate to 13,9% in line with market rates . After five years the present value of the loan is R682081,77. With the new interest rate , his monthly payments will increase by ?

Answer 1

If the present value of the loan is R911012 to be repaid after 12 years with an interest rate of 12.4% but to be changed to a new rate of 13.9% after the fifth year of starting, the monthly payments for the first five years is:

$Pmt=\frac{PV}{[\frac{1-(1+\frac{r}{m})^{-(mn)}}{\frac{r}{m}}]}$

$Pmt=\frac{R911012}{[\frac{1-(1+\frac{12.4\%}{12})^{-(12×5)}}{\frac{12.4\%}{12}}]}$

$Pmt=R20450$

After the fifth year, the interest rate changes to 13.9%, the present value becomes R682018.77 and n becomes 7

$\therefore Pmt=\frac{R682081.77}{[\frac{1-(1+\frac{13.9\%}{12})^{-(12×7)}}{\frac{13.9\%}{12}}]}$

$Pmt=R12745$

David's monthly payments decreases by R7705 (R20450-R12745).