At what rate percentage per annum (correct to one place of decimal) will ₹17,280 amount to ₹23,520 in 2 years, if the interest is compounded annually?

Given:

Principal (P) = ₹17,280

Amount (A) = ₹23,520

Time (t) = 2 years

Formula used:

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

Where, r = rate

Calculations:

23,520 = 17,280\((1+\frac{r}{100})^2\)

⇒ \(\frac{23,520}{17,280}= (1+\frac{r}{100})^2\)

⇒ \(\frac{136}{100}= (1+\frac{r}{100})^2\)

⇒ \(\sqrt{\frac{136}{100}}= (1+\frac{r}{100})\)

⇒ \(\frac{11.66}{10}= (1+\frac{r}{100})\)

⇒ \(\frac{11.66}{10}-1= \frac{r}{100}\)

⇒ \(\frac{1.66}{10}= \frac{r}{100}\)

⇒ r = 16.6%

∴ The correct answer is option (2).