Question

- If the amount received at the end of 2nd and 3rd year at Compound Interest on a certain Principal is Rs 22472, and Rs 23820.32 respectively, what is the rate of interest?

Answer 1

The rate of interest of this question is 5%

Answer 2

Answer:

Rate of Interest = 6% per annum

Step-by-step explanation:

Principal = P

Time = 2 year

Compound Interest = Rs 22472

Rate = r

n = no. of times the interest is compounded in 1 year

So, n = 1

$\text{Compound Interest = }P\times (1+\frac{r}{100\times n})^{n\times Time}\\\\22472 = P\times (1+\frac{r}{100})^2.........(1)$

Now, for time = 3 year , Compound Interest = Rs. 23820.32

$\text{Compound Interest = }P\times (1+\frac{r}{100\times n})^{n\times Time}\\\\23820.32 = P\times (1+\frac{r}{100})^3...........(2)$

Now, dividing compound interest for 3 years by compound interest of 2 years ( Or divide equation (2) by equation (1) ). We get ,

$\frac{P\times (1+\frac{r}{100})^3}{P\times (1+\frac{r}{100})^2}=\frac{23820.32}{22472}\\\\\implies 1+\frac{r}{100}=1.06\\\\\implies \frac{r}{100}=0.06\\\\\bf\implies r=6\%$

Hence, Rate of Interest = 6% per annum