Let's break down the problem: - **Success Ratio:** 10% - **Required Portfolio Rate of Return:** 19.4% - **Loan Amount:** $101,000 - **Loan Length:** 5 years ### Step 1: Find the Required Return per Successful Investment Since only 10% of investments are successful, each successful investment must compensate for the failures and still deliver a 19.4% return to the portfolio as a whole. Let \( r \) be the required rate of return per successful investment. The expected return across all investments should be 19.4%, so: \[ 0.10 \times (1 + r)^5 + 0.90 \times 0 = (1 + 0.194)^5 \] But this form is not correct. Let's clarify: For every $1 invested: - 10% of the time, you get back \((1 + r)^5\) - 90% of the time, you get $0 Expected value after 5 years = \(0.10 \times (1 + r)^5\) We want this expected value to be equal to the required return for the portfolio, i.e., to grow at 19.4% per year for 5 years: \[ (1 + 0.194)^5 = 2.4484 \] So, \[ 0.10 \times (1 + r)^5 = 2.4484 \] \[ (1 + r)^5 = \frac{2.4484}{0.10} = 24.484 \] \[ 1 + r = (24.484)^{1/5} \] \[ 1 + r = 1.8857 \] \[ r = 0.8857 \] So, the annual percentage rate \( r \) is **88.57%**. ### Final Answer: \[ \boxed{88.5700\%} \] (Rounded to four decimal places.)