Question

Find the sum on which the difference between the simple interest and compound interest at the rate of 8% per annum compounded annually be 64 in 2 years

Answer 1

Given :

Rate = 8%

Time = 2 years

Difference= 64

To Find :

The Sum.

Solution:

$Let \: sum \: be \: Rs \: x$

Simple Interest (SI) :

$= > \dfrac{x \times 8 \times 2}{100}$

$= > \dfrac{4x}{25} = 0.16x$

Compound Interest (CI):

For First Year:

$= > \dfrac{x \times 8 \times 1}{100} = 0.08x$

$= > 0.08x + 1 = 1.08x$

For Second Year:

$= > \dfrac{1.08x \times 8 \times 1}{100} = 0.864x$

Total Compound Interest :

$= > 0.08x + 0.0864x$

$= > 0.1664x$

The difference between the simple interest and the compound interest at the rate of 8% per annum compounded annually be 64 in 2 years.

Finding the Sum :

Simple Interest - Compound Interest = 64

$= > 0.16x - 0.1664x = 64$

$= > 0.0064x = 64$

$= > x = \dfrac{0.0064}{64}$

$= > x = 10000$

Hence, the sum is Rs 10,000