To determine the future value of a deposit of [tex]\(\$15,000\)[/tex] at an interest rate of 7% per year over a period of three years, we can use the future value formula:
[tex]\[
\text{future value} = P \times (1 + i)^t
\][/tex]
where:
- [tex]\(P\)[/tex] is the principal amount (initial deposit) which is [tex]\(\$15,000\)[/tex],
- [tex]\(i\)[/tex] is the annual interest rate, expressed as a decimal, so [tex]\(i = 0.07\)[/tex],
- [tex]\(t\)[/tex] is the time in years.
Substituting the given values into the formula, we get:
[tex]\[
\text{future value} = 15,000 \times (1 + 0.07)^3
\][/tex]
Next, we calculate the term [tex]\((1 + 0.07)^3\)[/tex]:
[tex]\[
(1 + 0.07)^3 = 1.07^3
\][/tex]
Thus:
[tex]\[
\text{future value} = 15,000 \times 1.07^3
\][/tex]
After calculating [tex]\(1.07^3\)[/tex], we see that:
[tex]\[
1.07^3 \approx 1.225043
\][/tex]
Therefore:
[tex]\[
\text{future value} = 15,000 \times 1.225043 \approx 18375.645
\][/tex]
So, the future value of the \[tex]$15,000 deposit after three years will be approximately \$[/tex]18,375.645.
Thus, the correct answer is:
[tex]\[
\text{A. } \$18,375.65
\][/tex]
