To calculate the maturity value of a simple interest loan, we use the formula:
[tex]\[ A = P(1 + rt) \][/tex]
where:
- \( P \) is the principal amount (initial amount of the loan)
- \( r \) is the annual interest rate (as a decimal)
- \( t \) is the time period in years
Given:
- \( P = \$14,000 \)
- \( r = 8.4\% \)
- \( t = 4 \text{ months} \)
Let's break it down step-by-step:
1. Convert the interest rate to a decimal:
[tex]\[
r = 8.4\% = \frac{8.4}{100} = 0.084
\][/tex]
2. Convert the time period into years:
[tex]\[
t = \frac{4 \text{ months}}{12 \text{ months/year}} = \frac{4}{12} = \frac{1}{3} \approx 0.3333
\][/tex]
3. Substitute the values into the formula:
[tex]\[
A = 14000 \left(1 + 0.084 \times 0.3333\right)
\][/tex]
4. Calculate the value inside the parentheses:
[tex]\[
1 + 0.084 \times 0.3333 = 1 + 0.028 = 1.028
\][/tex]
5. Multiply by the principal amount \( P \):
[tex]\[
A = 14000 \times 1.028 = 14392.0
\][/tex]
So, the maturity value of the simple interest loan, rounded to two decimal places, is:
[tex]\[
\boxed{14392.00}
\][/tex]
Thus, the answer is $14,392.00.
