Question

the compound interest on a certain sum for 2years and 6months at 5% per annum compounded annually is rs416. 20.find the sum.

Answer 1

2 years 6 months = 2+6/12 =
$2 \frac{1}{2} \: = x \frac{y}{z}$
$amount = p {(1 + \frac{r}{100})}^{x} \times (1 + \: \frac{r}{10} \times \frac{y}{z} )$
Amount = P((1+r/100)^2 ×(1+ r/100 ×1/2 )

P(1 + 5/100)^2 × (1 + 5/100 ×1/2)

=P(21/20)^2 × (41/40)

=P(21/20 ×21/20 ×41/40)

Amount =P ×(18081/16000)



We know

amount = sum +interest

P(18081/16000) = P+ 416.20

P(2081/ 16000) = 416.20

P= (416.20 ×16000)/2081

P= 3200
So the sum is
$sum = 3200$