What is the future value of \$5,500 invested for 17 years at an APR of 8.4\% compounded semiannually? (Round your answer to the nearest dollar.)

• A. \$19,870
• B. \$22,349
• C. \$18,120
• D. \$21,105

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the formula for future value with compound interest, which is \( FV = PV \times (1 + \frac{r}{n})^{n \times t} \), where \( FV \) is the future value, \( PV \) is the present value (initial investment), \( r \) is the annual interest rate (APR), \( n \) is the number of compounding periods per year, and \( t \) is the number of years.
2. Step 2: Identify the values given in the problem: \( PV = 5500 \), \( r = 8.4\% = 0.084 \), \( n = 2 \) (since interest is compounded semiannually), and \( t = 17 \).
3. Step 3: Substitute the values into the formula: \( FV = 5500 \times (1 + \frac{0.084}{2})^{2 \times 17} \).
4. Step 4: Simplify the expression inside the parentheses: \( 1 + \frac{0.084}{2} \), which represents the growth factor per compounding period.
5. Step 5: Calculate the exponent \( 2 \times 17 \) to determine the total number of compounding periods, then raise the growth factor to this power and multiply by \( PV \) to find the future value.