Step 1: 
To calculate the future value of an investment compounded annually, use the formula: 
\[A = P \left ( 1 + \frac { r} { n} \right ) ^ { nt} \]

Where: 
- \(A\) is the amount of money accumulated after n years, including interest. 
- \(P\) is the principal amount (the initial amount of money). 
- \(r\) is the annual interest rate (decimal). 
- \(n\) is the number of times that interest is compounded per year. 
- \(t\) is the number of years the money is invested for.

Step 2:

Given: 
- \(P = 15,000\) 
- \(r = 0.15\) 
- \(n = 1\) (compounded annually) 
- \(t = 5\)

Step 3:

Plug these values into the formula: 
\[A = 15,000 \left ( 1 + \frac { 0.15} { 1} \right ) ^ { 1 \times 5} \] 
\[A = 15,000 \left ( 1 + 0.15\right ) ^ 5\] 
\[A = 15,000 \left ( 1.15\right ) ^ 5\] 
\[A = 15,000 \times 2.011357\] 
\[A \approx 30,170.36\]

Step 4:

Thus, the future value is approximately $30,170.36, which matches option B.

Supplemental Knowledge:

Compound interest is a powerful concept in finance that refers to the process of earning interest on both the initial principal and the accumulated interest from previous periods. The formula for compound interest is:

\[A = P \left ( 1 + \frac { r} { n} \right ) ^ { nt} \]

where: 

- \(A\) is the amount of money accumulated after n years, including interest. 
- \(P\) is the principal amount (the initial amount of money). 
- \(r\) is the annual interest rate (decimal). 
- \(n\) is the number of times that interest is compounded per year. 
- \(t\) is the number of years the money is invested for.

Life in Context:

Imagine investing $15,000 with an annual compound interest rate of 15% in a savings account that accrues compound interest annually, understanding compound interest helps predict how your investments will perform over time and can guide financial decisions that align with your long-term financial goals.

When saving for major purchases or retirement, understanding how your money will expand with compound interest is invaluable in setting realistic savings targets and timelines.

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