# Sudhir lent Rs. 2,000 at compound interest at 10% payable yearly, while Prashant lent Rs. 2,000 at compound interest at 10% payable half-yearly. Find the difference in the interest received by Sudhir and Prashant at the end of one year.

Given:

Sudhir lent Rs. 2,000 at compound interest at 10% payable yearly.

Prashant lent Rs. 2,000 at compound interest at 10% payable half-yearly.

To find: Here we have to find the difference in the interest received by Sudhir and Prashant at the end of one year.

Solution:

Sudhir lent Rs. 2000 at compound interest at 10% payable yearly.

P = 2000, R = 10%, n = 1

We know that,

$A\ =\ P\left( 1\ +\ \frac{r}{100}\right)^{n}$

$A\ =\ 2000\left( 1\ +\ \frac{10}{100}\right)^{1}$

$A\ =\ P\left( \frac{110}{100}\right)$

A = Rs. 2200

Calculating compound interest:

C.I = A $-$ P

C.I = 2200 $-$ 2000

C.I = Rs. 200

Prashant lent ₹2000 at compound interest at 10% payable half-yearly:

P = 2000, R = 10% = 5% {half-yearly}, n = 2

$A\ =\ P\left( 1\ +\ \frac{r}{100}\right)^{n}$

$A\ =\ 2000\left( 1\ +\ \frac{5}{100}\right)^{2}$

$A\ =\ 2000\left( \frac{105}{100}\right)^{2}$

$A\ =\ 2000(1.05)^{2}$

A = Rs. 2205

Calculating compound interest:

C.I = A $-$ P

C.I = 2205 $-$ 2000

C.I = Rs. 205

Difference in the interest received by Sudhir and Prashant = Rs. 205 $-$ 200

Difference in the interest received by Sudhir and Prashant = Rs. 5

So, the difference in the interest received by Sudhir and Prashant is Rs. 5.