Find the total amount (in ₹) on ₹4,500 at 12% per annum for 2 years and 8 months compounded annually.

Correct option is B

Given:

Principal (P) = ₹4,500
Rate of interest (R) = 12% per annum
Time (T) = 2 years and 8 months
Formula Used:
For compound interest compounded annually, the formula for the total amount (A) is:
​$$A = P \left(1 + \frac{R}{100}\right)^T$$​
Solution:
2 years and 8 months = 2 +$$\frac{8}{12} = 2 + \frac{2}{3} = \frac{8}{3}$$​  years.
Since compounding is annual, we first calculate the amount for 2 full years, and

then add simple interest for the remaining 8 months on the amount obtained after 2 years.
Amount after 2 years (A₂):
​$$A_2 = P \left(1 + \frac{R}{100}\right)^2 = 4500 \left(1 + \frac{12}{100}\right)^2$$​​
​$$A_2 = 4500 \times (1.12)^2 = 4500 \times 1.2544 = ₹5,644.80$$​​
Simple Interest for the remaining 8 months (SI):
​$$\text{SI} = A_2 \times \frac{R}{100} \times \frac{8}{12} = 5644.80 \times \frac{12}{100} \times \frac{2}{3}$$​​
​$$\text{SI} = 5644.80 \times 0.12 \times \frac{2}{3} = 5644.80 \times 0.08 = ₹451.584 \approx ₹451.58$$​​
A =$$A_2 + \text{SI} =$$​5644.80 + 451.58 = ₹6,096.38
Alternate Method:
​$$A = P \left(1 + \frac{R}{100}\right)^{\text{whole years}} \times \left(1 + \frac{\text{fractional year} \times R}{100}\right)$$​​

​$$A = 4500 \times (1.12)^2 \times \left(1 + \frac{\frac{2}{3} \times 12}{100}\right) = 4500 \times 1.2544 \times 1.08$$​​
​$$A = 4500 \times 1.2544 \times 1.08 \approx ₹6,096.38$$​