Let's break down the problem: - **Success ratio:** 10% (so only 1 out of 10 investments succeeds) - **Required rate of return:** 19.4% (for the entire portfolio) - **Loan amount:** $101,000 - **Loan term:** 5 years The required rate of return (portfolio return) is based on the fact that only 1 out of 10 loans will succeed and return money to the lender. This means that the successful loan must return enough to cover all 10 loans plus the required return. #### Step 1: Find the future value needed from a successful loan Let **r** be the annual rate charged to the successful borrower. For the portfolio to earn a 19.4% annual return over 5 years: \[ FV_{portfolio} = PV \times (1 + 0.194)^{5} \] \[ FV_{portfolio} = \$101,000 \times (1 + 0.194)^{5} \] \[ FV_{portfolio} = \$101,000 \times (2.4317) \] \[ FV_{portfolio} = \$245,601.70 \] #### Step 2: Relate the required return to the success ratio Since only 1 out of 10 loans succeeds: \[ \text{Amount to be repaid by successful borrower} = \$245,601.70 \times 10 = \$2,456,017 \] But that's not correct; instead, the successful borrower must cover the whole portfolio's future value. Since only 1 out of 10 pays back, the return from the successful one must be 10 times the required future value: So, for a single successful loan: \[ \text{Amount to be repaid by successful borrower} = \$101,000 \times (1 + r)^{5} \] Set this equal to 10 times the required portfolio future value: \[ \$101,000 \times (1 + r)^{5} = 10 \times \$245,601.70 \] \[ \$101,000 \times (1 + r)^{5} = \$2,456,017 \] \[ (1 + r)^{5} = \frac{2,456,017}{101,000} \] \[ (1 + r)^{5} = 24.3 \] \[ 1 + r = (24.3)^{1/5} \] \[ 1 + r = 1.8921 \] \[ r = 0.8921 \] So, the **annual percentage rate** you would have to pay is: \[ \boxed{89.21\%} \] (Rounded to 4 decimal places: **89.2100%**)