Question

Simple interest on a sum of money for 2 years at 4% is Rs. 450. Find compound interest on the same sum and at the same rate for 1 year, if the interest is reckoned half yearly.

Answer 1

1^st case

Given:  S.I. = Rs. 450; Time = 2 years and Rate = 4%

∴ Principle = `[ "I" xx 100 ]/[ "R" xx "T"]`

= `[ 450 xx 100 ]/[ 4 xx 2 ]`

= Rs. 5625

2^nd case (compounded half-yearly)

P = Rs. 5,625; n = 1 year and r = 4%

∴ A = P`(1 + r/[ 2 xx 100 ])^( n xx 2)`

= `5625(1 + 4/[ 2 xx 100 ])^(1 xx 2)`

= `5625(51/50)^2`

= Rs. 5852.25

∴ C.I. = 5852.25 - 5625

= Rs. 227.25