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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.
Solution
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%
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