To calculate how much Frank will owe after 7 years, we use the formula for compound interest:

$A = P \times \left(1 + \frac{r}{n}\right)^{n \cdot t}$

Where:

• $A$ is the amount owed (future value),
• $P = 8000$ is the principal (initial amount borrowed),
• $r = 0.11$ is the annual interest rate (11%),
• $n = 2$ is the number of compounding periods per year (semiannually),
• $t = 7$ is the time in years.

Step 1: Substitute the values into the formula

$A = 8000 \times \left(1 + \frac{0.11}{2}\right)^{2 \cdot 7}$

Step 2: Simplify the terms

• Calculate $\frac{0.11}{2}$: $\frac{0.11}{2} = 0.055$

• Add 1 to get the base of the exponent: $1 + 0.055 = 1.055$

• Calculate the total number of compounding periods: $2 \cdot 7 = 14$

Step 3: Calculate $1.055^{14}$

Using a calculator: $1.055^{14} \approx 2.057648009$

Step 4: Multiply by the principal

$A = 8000 \times 2.057648009 \approx 16461.18407$

Step 5: Round to the nearest cent

$A \approx 16461.18$

Final Answer:

Frank will owe $16,461.18 after 7 years.

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Would you like me to explain any steps further or help with similar problems? Here are 5 related questions:

1. What would the amount be if the interest rate were 12% instead of 11%?
2. How would the amount change if interest were compounded quarterly instead of semiannually?
3. Can we calculate the effective annual rate (EAR) for the semiannual compounding?
4. How much interest would Frank have paid after 7 years?
5. How would the formula adapt if Frank made monthly payments?

Tip: Always double-check the number of compounding periods and ensure the rate is divided properly.