Ramu invested some money in HDFC at 4% per annum rate of interest. What would be the corresponding simple interest (in Rs. ) if after 2 years, Ramu got Rs. 127.5 as compound interest, considering annual compounding?

Correct option is C

Given:

Interest rate = 4% per annum

Time period = 2 years

Compound interest (CI) = Rs. 127.5

Interest is compounded annually.

Formula Used:

The formula for compound interest (CI) is:

CI = $$P \left(1 + \frac{r}{100}\right)^t - P$$​​

Where:

P is the principal amount

r is the rate of interest per annum

t is the time period in years

CI is the compound interest

For simple interest (SI):

SI = $$\frac{P \times r \times t}{100}$$​​

Solution:

Using the formula for CI:

$$127.5 = P \left(1 + \frac{4}{100}\right)^2 - P \\ \ \\ 127.5 = P \left(1.04^2 - 1\right) \\ \ \\ 127.5 = P \left(1.0816 - 1\right)\\ \ \\ 127.5 = P \times 0.0816 \\ \ \\ P = \frac{127.5}{0.0816} = 1562.5$$​​

Now, 

SI = $$\frac{1562.5 \times 4 \times 2}{100}$$​​

​$$= \frac{12500}{100} = 125$$​​

Thus, the corresponding simple interest is Rs. 125.