Let's break down the problem and solve step by step: ### Given: - **Success ratio**: 10% (Only 1 in 10 investments succeed) - **Required portfolio rate of return**: 19.4% - **Loan period**: 5 years - **Loan amount**: $101,000 ### **Step 1: Calculate the required payoff per successful investment** Since only 1 in 10 investments is successful, the successful investment must cover the losses of the 9 unsuccessful investments, plus provide the required rate of return. Let \( X \) be the payoff amount required from the successful investment after 5 years. - Total outlay for 10 investments: \( 10 \times \$101,000 = \$1,010,000 \) - Required return after 5 years: \( \$1,010,000 \times (1 + 0.194)^5 \) This must be the amount received from the one successful investment (the rest are worth $0): \[ X = \$1,010,000 \times (1 + 0.194)^5 \] \[ (1 + 0.194)^5 = (1.194)^5 \approx 2.4231 \] \[ X = \$1,010,000 \times 2.4231 \approx \$2,447,331 \] ### **Step 2: Find the annual percentage rate (APR) the successful borrower must pay** The successful borrower must repay $2,447,331 after 5 years on a $101,000 loan. The APR \( r \) is found by solving: \[ 101,000 \times (1 + r)^5 = 2,447,331 \] \[ (1 + r)^5 = \frac{2,447,331}{101,000} \approx 24.2251 \] \[ 1 + r = (24.2251)^{1/5} \approx 1.8915 \] \[ r = 1.8915 - 1 = 0.8915 \] \[ r = 89.15\% \] ### **Final Answer** \[ \boxed{89.1500\%} \] Enter this value rounded to four decimal places.