Question : What is the difference between the compound interest and the simple interest on Rs. 2,000 at 10% interest per annum for 2 years, if, for compound interest, interest is compounded annually?
Option 1: Rs. 20
Option 2: Rs. 40
Option 3: Rs. 80
Option 4: Rs. 60
Correct Answer: Rs. 20
Solution :
The formula for simple interest (SI) is, SI = $\frac{\text{PRT}}{100}$
where P is the principal amount, R is the rate of interest per annum (in decimal) and T is the time in years
SI = 2000 × 0.10 × 2 = Rs. 400
The formula for compound interest (CI) is, CI = P(1 + R)
T
– P
So, the compound interest is:
CI = 2000 × (1 + 0.10)
2
– 2000 = 2000 × 0.21 = Rs. 420
The difference between the compound interest and the simple interest is,
= CI – SI = 420 – 400 = Rs. 20
Hence, the correct answer is Rs. 20.
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