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
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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