Let's break down the problem: - **Success ratio**: 10% (only 1 in 10 investments succeed) - **Required rate of return**: 19.4% (on the overall portfolio) - **Loan term**: 5 years - **Loan amount**: $101,000 The required return of 19.4% is on the **whole portfolio**, but since only 10% of loans succeed, the loans that do succeed must generate enough return to cover all losses and still yield 19.4% overall. ### Step 1: Calculate the Required Return from a "Successful" Loan Let **x** be the annual percentage rate (APR) the investor must charge on a successful loan. Because only 1 out of 10 loans succeed, the money returned from that one success must cover: - The principal for 10 loans ($101,000 × 10 = $1,010,000) - The desired return of 19.4% per year over 5 years on the $1,010,000 So, after 5 years, the investor wants: \[ \text{Future Value} = \$1,010,000 \times (1 + 0.194)^{5} \] This amount must come from a single successful loan. So this is the payoff for one $101,000 loan after 5 years: \[ \text{Payoff} = \$1,010,000 \times (1.194)^{5} \] ### Step 2: Calculate the Required Future Value for One Successful Loan \[ (1.194)^{5} = 2.4334 \] \[ \$1,010,000 \times 2.4334 = \$2,457,734 \] So, after 5 years, the successful loan must pay **$2,457,734**. ### Step 3: Find the APR (Annual Rate) for the Loan Let \( r \) be the annual rate required on one successful $101,000 loan: \[ \$101,000 \times (1 + r)^{5} = \$2,457,734 \] \[ (1 + r)^{5} = \frac{2,457,734}{101,000} = 24.334 \] \[ 1 + r = (24.334)^{1/5} \] Find the 5th root of 24.334: \[ 1 + r = 1.8880 \] \[ r = 1.8880 - 1 = 0.8880 \] \[ r = 88.80\% \] ### **Answer** The annual percentage rate (APR) you would have to pay is: \[ \boxed{88.80\%} \] (Rounded to four decimal places: **88.7997%**)