Question

Sudhir lent 2000 at compound interest at 10%
payable yearly, while Prashant lent 2000 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.
​

Answer 1

Given:

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

Prashant lent Rs. 2000/- at compound interest at 10% payable half-yearly

To Find:

Difference in the interest received by

Sudhir and Prashant at the end of one year.

Solution:

Sudhir Case:

Principal (P) = Rs. 2000/-

Rate (r) = 10%

Number of times interest applied per time period (n) = 1

Time period = 1 year

Using Compound interest formula:

A = P( 1 + r/n )^nt

A = 2000( 1 + 10/100)¹

A = 2000( 110/100 )

A = Rs. 2200/-

Prashant Case:

Principal (P) = Rs. 2000/-

Rate (r) = 10%

Number of times interest applied per time period (n) = 2

Time period = 1 year

Using Compound interest formula:

A = P( 1 + r/n )^nt

A = 2000( 1 + 10/100×2)²

A = 2000( 105/100 × 105/100)

A = Rs. 2205/-

Difference in the interest received by Sudhir and Prashant at the end of one year :-

= 2205 - 2200

= Rs. 5/-

Hence, Rs. 5/- is the required answer.

Answer 2

Required answer -

It is given that ,

★ Sudhirr lent 2000 at compound interest at 10%  payable yearly

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

And we have to find,

★ the difference in the interest received by  Sudhir and Prashant at the end of one year.

So let's solve it !

Sudhir amount ,

Given

• Principal (p) = 2000rs
• Rate (r) = 10 %
• Time (n) = 1 year

so , as we know that ,

$\sf \Longrightarrow Amount =Principal (\dfrac{1+Rate}{100})^{n}$

$\sf \Longrightarrow Amount =2000 (\dfrac{1+10}{100})^{1}$

$\sf \Longrightarrow Amount =2000 (\dfrac{110}{100})$ LCM = 100

$\sf \Longrightarrow Amount =2200 \: rs$

Prashant amount ,

Given

• Principal (p) = 2000rs
• Rate (r) = 10 % half yearly

so , Rate = 10/2 % half yearly = 5%

• Time (n) = 2 year

so , as we know that

$\sf \Longrightarrow Amount =Principal (\dfrac{1+Rate}{100})^{n}$

$\sf \Longrightarrow Amount =2000 (\dfrac{1+5}{100})^{2}$

$\sf \Longrightarrow Amount =2000 (\dfrac{105}{100})^{2}$    LCM = 100

$\sf \Longrightarrow Amount =2000 (\dfrac{105}{100}*\dfrac{105}{100})$

$\sf \Longrightarrow Amount =2205 \: rs$

Now we know the amount of Sudhir and Prashant .

so, difference in the interest received by  Sudhir and Prashant at the end of one year = 2205 rs - 2200 rs = 5 rs