Question

Find the difference between the compound interest compounded yearly and half-yearly on Rs. 10,000 for 18 months at 10% per annum.

Answer 1

Given: P = Rs. 10,000 ; n = 18 months = `1 1/2` year and r = 10% p.a.

For First year

I = `(10,000xx10xx1)/100`

= 1,000

A = 10,000 + 1,000

= 11,000

For Second year,

P = 11,000, r = 10%, n = `1/2` year

I = `(11,000xx10xx1/2)/100`

= 550 

A₂ = 11,000 + 550

= 11,550

C.I. = A – P 

= 11,550 – 10,000

= 1,550 

When interest is compounded half-yearly

`A = P (1 + r/200)^(nxx2)`

= `10,000 (1 + 10/200)^(3/cancel2 xxcancel2`

 =`10,000 xx 21/20 xx 21/20 xx 21/20`

= `(105 xx 441)/4`

= `46305/4`

 = 11576.25

Compound interest yearly = 11576.25 – 10,000

= 1576.25

 Therefore, the difference between both C.I

= 1576.25 – 1,550

= 26.25