Question

The difference between C.I. and S.I. on Rs. 7,500 for two years is Rs. 12 at the same rate of interest per annum. Find the rate of interest.

Answer 1

Given: P = Rs. 7,500 and Time(n) = 2 years

Let rate of interest = y%

∴ S.I. = `[ "P" xx "R" xx "T" ]/100` 

= `[7500 xx y xx 2]/100` 

= Rs. 150y

∴ C.I. = P`(1 + r/100)^n - "P"` 

= `"Rs". 7,500( 1 + y/100 )^2 - "Rs."  7,500`

Given: C.I. : S.I. = Rs. 12

⇒ `7,500[ 1 + y/100 ]^2 - 7,500 - 150y = 12`

⇒ `7,500[ 1 + y^2/10000 + (2y)/100 ] - 7,500 - 150y = 12`

⇒ `7,500 + [7500y^2]/[10000] + 150y - 7,500 - 150y = 12`

⇒ `(3y^2)/4 = 12`

⇒ y² = 16          

⇒ y = 4%