Question : A sum of money is paid back in two annual instalments of Rs. 17,640 each, allowing 5% Compound interest compounded annually. The sum borrowed was:
Option 1: Rs. 32,800
Option 2: Rs. 32,200
Option 3: Rs. 32,000
Option 4: Rs. 32,400
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Correct Answer: Rs. 32,800
Solution :
Given: Installment = Rs. 17,640
Rate = 5%
Total installments = 2
1st instalment includes 5% interest on the given instalment.
Required sum borrowed = 1st installment + 2nd installment
$P(1+\frac{5}{100})^2= 17640(1+\frac{5}{100})+17640$
⇒ $P(\frac{105}{100})^2 = 17640(1+\frac{5}{100}+1)$
⇒ $P = 17640×\frac{205}{100}×\frac{100}{105}×\frac{100}{105}$
So, P = 32800
Hence, the answer is Rs. 32,800.
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