Suppose a bank gives an interest of 10% per annum compounded annually

Suppose a bank gives an interest of 10% per annum compounded annually for a fixed deposit for a period of two years. What should be the simple interest rate per annum if the maturity amount after two years is to remain the same?

10%

10.5%

11%

12%

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC CAPF – 2022

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Let the principal amount be P. For compound interest at 10% per annum compounded annually for 2 years, the maturity amount is $A_{CI} = P(1 + \frac{10}{100})^2 = P(1.1)^2 = 1.21P$. For simple interest over 2 years with an annual rate $R_{SI}$, the maturity amount is $A_{SI} = P + \text{Interest} = P + \frac{P \times R_{SI} \times 2}{100} = P(1 + \frac{2R_{SI}}{100})$. For the maturity amounts to be the same, $1.21P = P(1 + \frac{2R_{SI}}{100})$. Dividing by P (assuming P > 0), we get $1.21 = 1 + \frac{2R_{SI}}{100}$. Subtracting 1 from both sides, $0.21 = \frac{2R_{SI}}{100}$. Multiplying by 100, $21 = 2R_{SI}$. Therefore, $R_{SI} = \frac{21}{2} = 10.5$. The simple interest rate should be 10.5% per annum.

The problem requires comparing the maturity amounts obtained from compound interest and simple interest over the same period and finding the equivalent simple interest rate that yields the same amount.

Over a period of more than one year, compound interest will always yield a higher maturity amount than simple interest for the same principal and nominal rate, because interest earned in previous periods also earns interest. To get the same maturity amount, the simple interest rate must be higher than the compound interest rate (except for the first year, where they are equal).

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