Question : The compound interest earned in two years at 15% per annum is Rs. 20,640. What is the sum invested (in Rs.)?
Option 1: 64000
Option 2: 60000
Option 3: 56000
Option 4: 52000
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Correct Answer: 64000
Solution : Rate, R = 15% Term, n = 2 years Total amount = Rs. 20,640 Let the sum invested be $P$. Compound interest after 2 years = $P[(1+\frac{R}{100})^{2} –1)]$ ⇒ $20640$ = $P[(1+\frac{15}{100})^{2} –1)]$ ⇒ $20640$ = $P[(\frac{115}{100})^{2} –1)]$ ⇒ $20640$ = $P[(\frac{23}{20})^{2} –1)]$ ⇒ $20640$ = $P(\frac{529}{400} –1)$ ⇒ $20640$ = $P(\frac{129}{400})$ ⇒ $P$ = $\frac{20640×400}{129}$ = $64000$ Hence, the correct answer is 64,000.
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