Question

The compound interest on a certain amount for two years is rs. 291.2 and the simple interest on the same amount is rs. 280. If the rate of interest is same in both the cases, find the principal amount

Answer 1

Step-by-step explanation:

rate%= 11.2/140*100=8%

principal= 140/8*100=1750

Answer 2

The Principal amount is 1750 Rs.

Step-by-step explanation:

Let the amount be P

We know that with principal amount P, the rate of interest r and the period n, the compound interest after n years is given by

$I=P(1+\frac{r}{100})^n-P$

And the simple interest is given by

$I'=\frac{nPr}{100}$

Given

I = 291.2

I' = 280

Therefore,

$P(1+\frac{r}{100})^2-P=291.2$

Let r/100 = t

Thus

$P(1+t)^2-P=291.2$

$\implies P(1+2t+t^2)-P=291.2$

$\implies Pt(2+t)=291.2$

Also

$2Pt=280$

$\implies Pt=140$

Therefore,

$140(2+t)=291.2$

$\implies 2+t=291.2/140$

$\implies 2+t=2.08$

$\implies t=0.08$

$\implies \frac{r}{100}=0.08$

$\implies r=8$ %

Therefore, the rate of interest is 8%

$Pt=140$

$\implies P=140/t$

$\implies P=140/0.08$

$\implies P=1750$ Rs.

Therefore, the principal amount is 1750 Rs.

Hope this helps.

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