​At what rate of compound interest per annum will a sum of ₹1,000 become ₹1,061 in 2 years?​

Correct option is A

Given:

Principal ($P$) = ₹1,000

Amount ($A$) = ₹1,061

Time ($t$) = 2 years

Formula Used: ​

Compound interest for amount;

$$A = P \left(1 + \frac{r}{100}\right)^t$$

​Solution:

$$1,061 = 1,000 \left(1 + \frac{r}{100}\right)^2$$

$$1.061 = \left(1 + \frac{r}{100}\right)^2$$

$$\sqrt{1.061} = 1 + \frac{r}{100}$$

​​$$\sqrt{1.061} - 1 =\frac{r}{100}$$

$${r}=(\sqrt{1.061} - 1) \times 100$$

​​r ≈ 3%

Thus, rate of interest per annum is 3%

Alternate Method:

P                      A

1000         :    1061

For 2 years, take square root

31.62         :     32.57

Rate of interest =   $$\frac{0.95 }{31.62}$$ $$\times$$ 100 ≈ 3%

A=P(1+r100)tA = P \left(1 + \frac{r}{100}\right)^t