Answer to Question #323483 in Financial Math for justice

Question

Round the answer to this question to the nearest rand. David borrowed R911012,00

R911012,00 to refurbish his holiday home. The loan requires monthly repayments over 12 years. When he borrowed the money, the interest rate was 12,4% per annum, compounded monthly, but five years later the bank increased the annual interest rate to 13,9%, in line with market rates. After five years the present value of the loan is R682081,77

R682081,77. With the new interest rate, his monthly payments will increase by

Answer 1

Periodic payments, given the present value is found as:

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

If the present value of the loan is R911012 to be repaid after 12 years with an interest rate of 12.4% , then the initial monthly payments will be

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

$Pmt=R12187$

If 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 increases by R558, i.e. $(R12745-R12187)$ .