Question

The compound interest fir 2 years and 3 years on a certain principal at certain rate of interest are ₹8820 and ₹9261 respectively. Find the rate of interest and the principal.

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Answer 1

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Answer 2

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Here is your answer
Let Sum = P
Rate of interest = R%
T =2 and 3 years
A = 8820 and 9261

As we know that the formula
A = P(1+ R/100)^t

So
$8820 = p(1 + \frac{r}{100} ) {}^{2}$
AND
$9261 = p(1 + \frac{r}{100} ) {}^{3}$
Now Divide 2 by 1 above equation we get
$\frac{9261}{8820} = (1 + \frac{r}{100} ) \\ 1.05 = \frac{100 + r}{100} \\ 100 + r = 1.05 \times 100 \\ r = 105 - 100 \\ r = 5\%$
Now put it in the equation 1 we get
$p( \frac{100 + 5}{100} ) {}^{2} = 8820 \\ p( \frac{105}{100} ) {}^{2} = 8820 \\ p(1.05) {}^{2} = 8820 \\ p = \frac{8820}{1.05 \times 1.05} \\ p = 8000$
Hence
Principal = Rs 8,000
Rate of interest = 5%


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