Question : A loan is to be returned in two equal yearly instalments. If the rate of interest is 10% p.a. compounded annually and each instalment is INR 5,808, then 60% of the total interest (nearest to INR) charged in this scheme is:
Option 1: 917
Option 2: 911
Option 3: 922
Option 4: 913
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Correct Answer: 922
Solution : Let the loan amount be P. Then using P = $\frac{\text{A}}{(1 +\frac{\text{R}}{100})^T}$, where A is amount due at R% rate of interest for $T$ years ⇒ P = $\frac{5808}{(1+\frac{10}{100})}$ + $\frac{5808}{(1+\frac{10}{100})^{2}}$ = $\frac{5808}{\frac{11}{10}}$ + $\frac{5808}{\frac{121}{100}}$ = $\frac{58080}{11}$ + $\frac{580800}{121}$ = 5280 + 4800 = 10080 Now, Interest = (2 × instalment – P) ⇒ Interest = (2 × 5808 – 10080) = (11616 – 10080) = 1536 So, 60% interest charged = 60% of 1536 = 921.6 $\approx$ INR 922 Hence, the correct answer is 922.
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