Question

A sum of money, invested at compound interest, amounts to Rs. $$19,360$$ in $$2$$ years and to Rs. $$23,425.60$$ in $$4$$ years. Find the original sum of money.

Solution

On interest being compounded for $$2$$ years, $$Amount = P{(1 + \frac {R}{100})}^{N}$$$$\implies 19,360 = P{(1 + \frac {R}{100})}^{2}$$  --- (1)On interest being compounded for $$4$$ years, $$Amount = P{(1 + \frac {R}{100})}^{N}$$$$\implies 23,425.60 = P{(1 + \frac {R}{100})}^{4}$$  --- (2)Dividing, eqn (2) by eqn (1)$$1.21 = {(1 + \frac {R}{100})}^{2}$$ Taking square root on both sides,$$1.1 = 1 + \frac {R}{100}$$$$\implies 0.1 = \frac {R}{100}$$$$\implies R = 10$$ % Putting the value of $$R$$ in eqn $$(1),$$ we get$$\implies 19,360 = P{(1 + \frac {10}{100})}^{2}$$ $$\implies19,360 = P \times {(1.1})^{2}$$ $$\implies P = \frac {19,360}{1.21}$$$$\implies P = Rs. 16,000$$Mathematics

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