Q.At an annual interest rate of 5%, what will be the difference between compound interest and simple interest for ₹20,000 over 2 years?

At an annual interest rate of 5%, the simple interest for ₹20,000 over 2 years is: \[ \cfrac{20000 \times 2 \times 5}{100} = ₹2000 \] The compound interest for ₹20,000 at the same rate for 2 years is: \[ = \left[20000 \left(1 + \cfrac{5}{100}\right)^2 - 20000\right] \] \[ = \left[20000 \left(\cfrac{105}{100}\right)^2 - 20000\right] \] \[ = \left[20000 \times \cfrac{105 \times 105}{100 \times 100} - 20000\right] \] \[ = \left[2 \times 105 \times 105 - 20000\right] = [22050 - 20000] = ₹2050 \] Therefore, the difference between compound interest and simple interest over 2 years is ₹50.
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