Question : The compound interest (compounding annually) on a certain sum for 2 years at the rate of 20 percent per annum is Rs. 2420. What will be the simple interest on the same sum for 3 years at the same rate of interest?
Option 1: Rs. 3300
Option 2: Rs. 3000
Option 3: Rs. 3800
Option 4: Rs. 4200
Correct Answer: Rs. 3300
Solution :
Using: Amount = $P×(1+\frac{R}{100})^{T}$ – P , where
P is the principal, R is the rate of interest, and T is the time in years.
According to the question
⇒ 2420 = P × (1+$\frac{20}{100})^{2}$ – P
⇒ 2420 = P×(1+$\frac{1}{5})^{2}$ – P
⇒ 2420 = P($\frac{6}{5})^{2}$ – P
⇒ 2420 = P($\frac{36}{25})$ – P
⇒ 2420 = $\frac{36P}{25}$ – P
⇒ 60500 = 11P
⇒ P = $\frac{60500}{11}$ = 5500
So, simple interest = $\frac{P×R×T}{100}$ = $\frac{5500×20×3}{100}$ = $\frac{330000}{100}$ = 3300
Hence, the correct answer is Rs. 3300.
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