Question : A man invested a sum of money at compound interest. It amounted to Rs. 2420 in 2 years and Rs. 2662 in 3 years. Find the sum:
Option 1: Rs. 1000
Option 2: Rs. 2000
Option 3: Rs. 5082
Option 4: Rs. 3000
Correct Answer: Rs. 2000
Solution :
Given: A man invested a sum of money at compound interest. It amounted to Rs. 2420 in 2 years and Rs. 2662 in 3 years.
Let the sum be p and the rate of interest per annum be r%.
Here, Rs. 2420 yield interest (2662 – 2420) = Rs. 242 in 1 year.
So the rate of interest r is = $\frac{242}{2420}×100$ = 10%
Now the sum p amounts to 2420 in 2 years at the compound interest rate of 10% per annum.
⇒ $p(1+\frac{10}{100})^2=2420$
⇒ $p(\frac{11}{10})^2=2420$
⇒ $p=2420×\frac{10}{11}×\frac{10}{11}=2000$
Hence, the correct answer is Rs. $2000$.
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