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].
