Let's break down the problem: **Given data:** - Blue Angel's portfolio required rate of return: **19.4%** - Success ratio: **10%** (only 10% of investments succeed) - Loan amount: **$101,000** - Loan duration: **5 years** **To Find:** The annual percentage rate (APR) you would have to pay for this loan. --- ### Calculation Steps **1. Required Rate of Return on the Portfolio:** - Blue Angel wants to achieve **19.4%** annual return on their **entire portfolio**. **2. Only 10% of loans succeed:** - Only 1 out of 10 loans will repay anything. - So, the successful loan has to generate enough return to cover itself **and the losses from the other 9 loans**. **3. Calculate the required return from the successful loan:** Let \( r \) be the annual percentage rate charged to successful loans. The future value (FV) required from the successful loan after 5 years: \[ FV = PV \times (1 + r)^5 \] But, on average, only 1 out of 10 loans will pay off. So, to get the portfolio return: \[ 0.1 \times PV \times (1 + r)^5 = PV \times (1 + 0.194)^5 \] Divide both sides by \( PV \): \[ 0.1 \times (1 + r)^5 = (1.194)^5 \] \[ (1 + r)^5 = \frac{(1.194)^5}{0.1} \] Calculate \( (1.194)^5 \): \[ (1.194)^5 \approx 2.4221 \] So, \[ (1 + r)^5 = \frac{2.4221}{0.1} = 24.221 \] \[ 1 + r = (24.221)^{1/5} \] \[ 1 + r \approx 1.8922 \] \[ r \approx 0.8922 \] So, \[ \boxed{r \approx 89.22\%} \] --- ### **Final Answer** **The annual percentage rate you would have to pay for this loan is:** \[ \boxed{89.22\%} \] (Rounded to four decimal places: **89.2200%**)