Find the Compound Interest on a sum of Rs. 1000 at the rate of 10% per annum for 1.5 years when interest is compounded half-yearly.

Correct option is D

Given:

Sum =  Rs. 1000

Rate = 10% per annum

Time = 1.5 years

Interest is compounded half-yearly.

Formula Used :

​$$\text{Amount} = \text {Principal} \left(1 + \frac{r}{100}\right)^{t}$$​​

Solution:

P = 1000, r = 10% and t = 1.5 years

If interest is compounded half-yearly.

R = 10/2 = 5% and Time = 1.5 × 2 = 3

As we know,

A = P (1 + r/100)^t

=> A = 1000 (1 + 5/100)³

=> A = 1000 × (21/20) × (21/20) × (21/20)

=> A = 1157.63

CI = A-P = 1157.63 – 1000 = 157.63

Alternate Method:

5% = 1/20

=> 20³= 21³

=> 8000 = 9261

=> 8000 unit = 1000

1 unit = 1000/8000 = 1/8

=> 9261 – 8000 = 1261

=> 1261 unit = 1261 × (1/8) = 157.625 $$\approx 157.63$$​