Question

Sangita lent 40,960 rupees to Amar to purchase a shop at 12.5% per annum.If the intrest is compounded semi annually.
Find the intrest paid by Amar after 1 1/2years.​

Answer 1

Answer:

17,360

Step-by-step explanation:

Rate =12.5% = 1 / 8

Int. compounded semi-annually

= 40960(9/8 ×9/8×9/8) - 40960

= 58320 - 40960 = 17360 (Ans.)

=

Answer 2

Given :

Principle : ₹40960

Rate of interest : 12.5%

Time 1½ years

To find :

The interest paid by Amar after the time period.

Solution :

First, we'll find the amount by it's formula.

Amount :

$\sf \dashrightarrow Amount = Principle \bigg( 1 + \dfrac{Rate}{100} \bigg)^{T2}$

$\sf \dashrightarrow 40960 \bigg( 1 + \dfrac{12.5}{100} \bigg)^{1.5(2)}$

$\sf \dashrightarrow 40960 \bigg( \dfrac{100 + 12.5}{100} \bigg)^{3}$

$\sf \dashrightarrow 40960 \bigg( \dfrac{112.5}{100} \bigg)^{3}$

$\sf \dashrightarrow 40960 \bigg( \dfrac{1125}{1000} \bigg)^{3}$

$\sf \dashrightarrow 40960 \bigg( \dfrac{9}{8} \bigg)^{3}$

$\sf \dashrightarrow 40960 \bigg( \dfrac{9^3}{8^3} \bigg)$

$\sf \dashrightarrow 40960 \bigg( \dfrac{729}{512}$

$\sf \dashrightarrow \dfrac{40960 \times 729}{512} = \dfrac{29859840}{512}$

$\sf \dashrightarrow \cancel \dfrac{29859840}{512} = 58320$

Now, we can find the compound interest.

Compound interest :

$\sf \dashrightarrow Amount - Principle$

$\sf \dashrightarrow 58320 - 40960$

$\dashrightarrow$₹$\sf 17360$

Hence, the interest paid by Amar at the end of 1½ years is ₹17360.