Question : Rajnish borrowed INR 1,500 from a bank and repaid the entire amount with interest in two equal annual instalments, the first instalment being paid a year after Rajnish borrowed from the bank. If the rate of interest was 40% per annum, compounded annually, then what was the value (in INR) of each instalment paid by Rajnish?
Option 1: 1125
Option 2: 1470
Option 3: 1225
Option 4: 1350
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Correct Answer: 1225
Solution :
Let the two equal instalments be $P_1$ and $P_2$
Given: $P_1 + P_2 = 1500$ and rate of interest $(R)= 40 \%$
Since annual instalments are equal,
So, $P_1(1+\frac{R}{100})=P_2(1+\frac{R}{100})(1+\frac{R}{100})$
⇒ $\frac{P_1}{P_2}=1+\frac{R}{100}=1+\frac{40}{100}=1+\frac{2}{5}=\frac{7}{5}$
⇒ $P_2 = \frac{5P_1}{7}$
Now, $P_1 + P_2 = 1500$
⇒ $P_1+\frac{5P_1}{7}= 1500$
⇒ $\frac{12P_1}{7}= 1500$
⇒ $P_1 = \frac{1500×7}{12}=875$
Installments = $P_1(1+\frac{R}{100})=875(1+\frac{40}{100})=875×\frac{7}{5}=1225$
Hence, the correct answer is 1225.
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