Question

If the difference between the compound interest compounded annually
and simple interest on a certain amount at 10% per annum for two
years is 372, then the principal amount is​

Answer 1

Given: The difference between the compound interest compounded annually and simple interest on a certain amount at 10% per annum for two years is 372.

To find: We have to find the principal.

Solution:

Let the principal be x rupees.

The compound interest on x rupees at 10% per annum for 2 years is given as-

$x {(1 + \frac{10}{100} )}^{2} - x$

The simple interest on x rupees at 10% per annum for 2 years is given as-

$\frac{x10 \times 2}{100}$

The difference between compound interest and simple interest is 372 rupees.

So, we can write-

$x {(1 + \frac{10}{100} )}^{2} - x - \frac{20x}{100} = 372 \\ x \times { \frac{11}{10} }^{2} - x - \frac{20x}{100} = 372 \\ \frac{121x}{100} - x - \frac{20x}{100} = 372 \\ \frac{121x - 100x - 20x}{100} = 372 \\ \frac{x}{100} = 372 \\ x = 37200$

The value of x is 37200.

Thus, the principal is 37200 rupees.