The interest earned by investing a sum of money in scheme A for two years is Z 450/- more than the interest earned when the same sum is invested in scheme B for the, same period. If schemes A and B both offer compound interest (compounded annually) a ?->(Show Answer!)

1. The interest earned by investing a sum of money in scheme A for two years is Z 450/- more than the interest earned when the same sum is invested in scheme B for the, same period. If schemes A and B both offer compound interest (compounded annually) at 30% p.a. and 20% p.a. respectively, what was the sum invested in each scheme ?

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By: anil on 05 May 2019 01.21 am

Let the amount invested in each scheme = Rs. $$P$$ Scheme A : $$C.I. = P [(1 + frac{R}{100})^T - 1]$$ = $$P [(1 + frac{30}{100})^2 - 1]$$ = $$P [(frac{13}{10})^2 - 1] = P [(frac{169}{100}) - 1]$$ = $$frac{69P}{100}$$ Scheme B : $$C.I. = P [(1 + frac{20}{100})^2 - 1]$$ = $$P [(frac{12}{10})^2 - 1] = P [(frac{144}{100}) - 1]$$ = $$frac{44P}{100}$$ Acc to ques, => $$(frac{69P}{100}) - (frac{44P}{100}) = 450$$ => $$frac{25P}{100} = 450$$ => $$P = 450 imes 4$$ = Rs. $$1,800$$

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