Question

A computer is sold either for Rs.19200 cash or for Rs.4800 cash down payment together with five equal monthly installments. If the rate of interest charged is $12\%$ per annum compounded annually, then the amount of each installment (nearest to a rupee) is:

Accepted Answer

B. Principal balance = $19200 - 4800 = 14400$. Monthly rate $r = 1\% = 0.01$. Sum of present values of 5 equal installments $I$: $I \left( \frac{1}{1.01} + \frac{1}{1.01^2} + \frac{1}{1.01^3} + \frac{1}{1.01^4} + \frac{1}{1.01^5} \right) = 14400$. Using $P = I \left[ \frac{1 - (1+r)^{-n}}{r} \right] \Rightarrow 14400 = I \left[ \frac{1 - 1.01^{-5}}{0.01} \right] \approx 4.85343 I$. $I \approx \frac{14400}{4.85343} \approx 2965$.

Installments and Compound Interest

Explanation

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