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A sum of money is borrowed and paid back in two annual installments of Rs. 1764 each, allowing 5% compound interest. What was the sum borrowed?1). Rs. 40002). Rs. 33403). Rs. 32804). Rs. 3200 |
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Answer» Let’s assume that the amount borrowed is Rs. P. Also, let each installment be Rs. A. Now, the total amount to be repaid at the end of given time period $(= P\;{\left( {1 + \frac{R}{{100}}} \right)^T})$ Also, total amount $( = A + A\left( {1 + \frac{R}{{100}}} \right) + A{\left( {1 + \frac{R}{{100}}} \right)^2})$ ….. till T terms In this case, A = 1764, R = 5 and T = 2 $(\THEREFORE P\;{\left( {1 + \frac{R}{{100}}} \right)^2} = A + A\left( {1 + \frac{R}{{100}}} \right) = A\left( {2 + \frac{R}{{100}}} \right))$ SUBSTITUTING the given values: $(\begin{array}{l} \Rightarrow P{\left( {1 + \frac{5}{{100}}} \right)^2} = 1764\;\left( {2 + \frac{5}{{100}}} \right)\\ \Rightarrow P \times \frac{{21}}{{20}} \times \frac{{21}}{{20}} = 1764 \times \frac{{41}}{{20}}\end{array})$ ⇒ P = 3280 |
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