Question : Priya borrowed a certain sum at the rate of 12% per annum. If she paid INR 10176 at the end of 2 years as interest compounded annually, what was the sum she borrowed?
Option 1: INR 30000
Option 2: INR 20000
Option 3: INR 50000
Option 4: INR 40000
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Correct Answer: INR 40000
Solution :
Rate, $R$ = 12%
Term, $n$ = 2 years
Compound interest = INR 10176
Let $P$ be the principal sum.
When compounded annually,
Compound interest = $P(1+\frac{R}{100})^{n}-P$
So, $10176 = P(1+\frac{12}{100})^{2}-P$
⇒ $10176 =P(1+\frac{3}{25})^{2}-P$
⇒ $10176 = P(\frac{28}{25})^{2}-P$
⇒ $10176 = P(\frac{28^2-25^2}{25^2})$
⇒ $10176 = P(\frac{159}{625})$
⇒ $P = \frac{10176×625}{159}=40000$
Hence, the correct answer is INR 40000.
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