Answer :

Sure, let's calculate the amount Nikhil has after 2 years with a 4% annual compound interest rate.

### Step-by-Step Solution:

1. Identify the principal amount (P):
The initial investment that Nikhil made is $200.

2. Determine the annual interest rate (r):
The annual interest rate given is 4%. In decimal form, this is 0.04.

3. Identify the time period (t):
The investment duration is 2 years.

4. Use the compound interest formula:
The compound interest formula is:

[tex]\[ A = P \times (1 + r)^t \][/tex]

where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial sum of money).
- [tex]\( r \)[/tex] is the annual interest rate (decimal).
- [tex]\( t \)[/tex] is the time the money is invested for in years.

5. Plug the values into the formula:

[tex]\[ A = 200 \times (1 + 0.04)^2 \][/tex]

6. Calculate the inside of the parentheses first:

[tex]\[ 1 + 0.04 = 1.04 \][/tex]

7. Raise the result to the power of 2:

[tex]\[ 1.04^2 \approx 1.0816 \][/tex]

8. Multiply the result by the principal (200):

[tex]\[ A = 200 \times 1.0816 = 216.32 \][/tex]

Thus, the exact amount Nikhil will have after 2 years is [tex]\( \boxed{216.32} \)[/tex].