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# 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.

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