Question Dale takes out a loan of \( \$ 8,000 \) with a \( 15.2 \% \) interest rate that is compounded semi-annually. If he pays off the loan in 3 years, how much will he end up paying? Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.

To determine the total amount Dale will pay off after 3 years on a loan of \$8,000 with a 15.2% annual interest rate compounded semi-annually, follow these steps: ### **1. Understand the Compounding Terms** - **Principal (P):** \$8,000 - **Annual Interest Rate (r):** 15.2% or 0.152 - **Compounding Frequency:** Semi-annually (twice a year) - **Number of Years (t):** 3 ### **2. Calculate the Interest Rate per Period** Since the interest is compounded semi-annually: \[ \text{Interest rate per period (i)} = \frac{0.152}{2} = 0.076 \text{ (or 7.6%)} \] ### **3. Determine the Total Number of Periods** \[ \text{Total periods (n)} = 2 \times 3 = 6 \text{ periods} \] ### **4. Use the Compound Interest Formula** The compound interest formula is: \[ A = P \times (1 + i)^n \] Substituting the known values: \[ A = 8000 \times (1 + 0.076)^6 \] ### **5. Calculate \((1 + 0.076)^6\)** First, compute the growth factor: \[ (1.076)^6 \approx 1.551934 \] ### **6. Calculate the Total Amount (A)** Multiply the principal by the growth factor: \[ A = 8000 \times 1.551934 \approx 12415.472 \] ### **7. Round to the Nearest Cent** \[ A \approx \$12,415.47 \] ### **Conclusion** Dale will end up paying **\$12,415.47** after 3 years.