Verified answer

To calculate the amount in Aditya's account at the end of each year, we can use the formula for compound interest:

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

Where:

- (A) is the amount at the end of the investment period.

- (P) is the principal amount (initial investment), which is $30,000 in this case.

- (r) is the annual interest rate, which is 10%.

- (n) is the number of years.

Let's calculate the amounts for each year:

(a) After one year:

[tex] \[ A = 30000 \times \left(1 + \frac{10}{100}\right)^1 = 30000 \times 1.1 = 33000 \] [/tex]

So, the amount in Aditya's account after one year will be 33,000.

(b) After two years:

[tex] [ A = 30000 \times \left(1 + \frac{10}{100}\right)^2 = 30000 \times 1.21 = 36300 \] [/tex]

The amount in his account after two years will be 36,300.

(c) After three years:

[tex] \[ A = 30000 \times \left(1 + \frac{10}{100}\right)^3 = 30000 \times 1.331 = 39930 \] [/tex]

The amount in his account after three years will be 39,930.