Question

The difference between compound interest and simple interest on an amount of Rs 15000 for 2 years is rupees 96 what is the rate of interest per annum

Answer 1

Let the rate of interest per annum be R%

Amount after 2 years on Rs.15000 when interest is compounded annually =P(1+R100)T=15000(1+R100)2Compound Interest =15000(1+R100)2−15000=15000[(1+R100)2−1]Simple Interest = PRT100=15000×R×2100=300RAmount after 2 years on Rs.15000 when interest is compounded annually =P(1+R100)T=15000(1+R100)2Compound Interest =15000(1+R100)2−15000=15000[(1+R100)2−1]Simple Interest = PRT100=15000×R×2100=300R

Difference between compound interest and simple interest = Rs.96

15000[(1+R100)2−1]−300R=9615000[1+2R100+(R100)2−1]−300R=9615000[2R100+(R100)2]−300R=96300R+15000(R100)2−300R=9615000(R100)2=9615000(R210000)=963(R22)=96R2=64R=815000[(1+R100)2−1]−300R=9615000[1+2R100+(R100)2−1]−300R=9615000[2R100+(R100)2]−300R=96300R+15000(R100)2−300R=9615000(R100)2=9615000(R210000)=963(R22)=96R2=64R=8

Rate of interest per annum = 8%