Question : The difference between the simple interest and the compound interest at the same rate for INR 32,000 for 2 years is 80. What is the rate of interest, if in the case of compound interest, interest is compounded annually?
Option 1: 8% per annum
Option 2: 2% per annum
Option 3: 5% per annum
Option 4: 12% per annum
Correct Answer: 5% per annum
Solution :
Principal amount = 32,000
Time = 2 years
Let R be the rate of interest per annum.
The difference between the simple interest and the compound interest = 80
Difference = $\frac{\text{P}\times{\text{R}}^2}{100^2}$
80 = $\frac{(32000 × \text{R}^2)}{100^2}$
⇒ R
2
= 25
Rate of Interest R = 5% per annum
Hence, the correct answer is 5% per annum.
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