What will be the amount if a sum of Rs. 8000 placed at compound interest for 3 years while the rate of interest for the first, second and third years is 5%, 6% and 7% respectively?

The correct option is 9527.28.

To find the total amount when a sum is placed at compound interest with different rates of interest for successive years, we use the general compound interest formula for varying rates:

$A=P\times \left(1+\frac{R_1}{100}\right)\times \left(1+\frac{R_2}{100}\right)\times \left(1+\frac{R_3}{100}\right)$

Where:
- $P$ is the principal amount = Rs. 8000
- $R_1$ is the rate of interest for the first year = 5%
- $R_2$ is the rate of interest for the second year = 6%
- $R_3$ is the rate of interest for the third year = 7%
- $A$ is the final amount after 3 years

Substituting the given values into the formula:

$A=8000\times \left(1+\frac{5}{100}\right)\times \left(1+\frac{6}{100}\right)\times \left(1+\frac{7}{100}\right)$

Simplify each factor inside the parentheses:

$A=8000\times 1.05\times 1.06\times 1.07$

Let us calculate the product step-by-step:

1. Find the value after the first year:
$8000\times 1.05=8400$

2. Find the value after the second year:
$8400\times 1.06=8904$

3. Find the final amount after the third year:
$8904\times 1.07=9527.28$

Therefore, the total amount after 3 years is Rs. 9527.28.