To determine the principal investment given the final amount after 5 years and an annual simple interest rate of 3.7%, we can follow these steps:
1. Identify the given variables:
- Final amount ([tex]\( A \)[/tex]) after 5 years: \[tex]$1,422
- Annual simple interest rate (\( r \)): 3.7% (expressed as a decimal, 0.037)
- Time duration (\( t \)): 5 years
2. Write down the formula for the total amount in a simple interest context:
\[
A = P(1 + rt)
\]
Where:
- \( P \) is the principal amount (initial investment)
- \( r \) is the annual interest rate in decimal form
- \( t \) is the time in years
- \( A \) is the amount after \( t \) years
3. Substitute the known values into the equation:
\[
1422 = P(1 + 0.037 \times 5)
\]
4. Simplify inside the parentheses:
\[
1422 = P(1 + 0.185)
\]
\[
1422 = P(1.185)
\]
5. Solve for the principal amount \( P \):
\[
P = \frac{1422}{1.185}
\]
6. Perform the division:
\[
P \approx 1200.0
\]
Thus, the principal investment amount is approximately \$[/tex]1,200.
Therefore, the correct answer is:
[tex]\[
\$1200
\][/tex]
