Question

At what rate of interest 1,200 becomes ₹ 1,323 in 2 years where interest gets compounded annually:

• A. \(2\frac{1}{2}\%\)
• B. \(3\frac{1}{4}\%\)
• C. 5%
• D. \(7\frac{1}{2}\%\)

Answer 1

The Correct Option is C

To determine the rate of interest at which ₹1,200 becomes ₹1,323 in 2 years with annual compounding, we use the compound interest formula:

\[A = P \left(1 + \frac{r}{100}\right)^n\]

• A = Final amount = ₹1,323
• P = Principal amount = ₹1,200
• n = Number of years = 2
• r = Rate of interest (unknown)

Substituting the known values into the formula, we get:

\[1,323 = 1,200 \left(1 + \frac{r}{100}\right)^2\]

Dividing both sides by 1,200:

\[\frac{1,323}{1,200} = \left(1 + \frac{r}{100}\right)^2\]

\[1.1025 = \left(1 + \frac{r}{100}\right)^2\]

Taking the square root of both sides:

\[\sqrt{1.1025} = 1 + \frac{r}{100}\]

\[1.05 = 1 + \frac{r}{100}\]

Subtracting 1 from both sides:

\[0.05 = \frac{r}{100}\]

Multiplying both sides by 100:

\[r = 5\]

Therefore, the rate of interest is 5%.