Let's break down the question and solve it step by step. **Given:** - Success ratio: 10% - Required portfolio return: 19.4% - Loan: $101,000 - Loan period: 5 years ### Step 1: Understanding the Risk Since only 10% of investments succeed, for every 1 successful investment, there are 9 unsuccessful ones (out of 10). ### Step 2: Required Return Calculation Blue Angel wants an overall return of 19.4% per year on its entire portfolio. Let \( r \) be the required annual percentage rate for a single successful loan. The investor will only get money back from the successful investments. That means, out of 10 loans of $101,000 each, only 1 will pay back anything; the others will be lost. The successful investment must pay back enough to cover all 10 investments **plus** the required return. ### Step 3: Formula Let’s calculate the required future value (FV) from one successful investment after 5 years. - Total amount invested in 10 loans: \( 10 \times \$101,000 = \$1,010,000 \) - Required portfolio value after 5 years: \( \$1,010,000 \times (1 + 0.194)^5 \) Now, all of this must come from the one successful investment: \[ \text{FV} = \$1,010,000 \times (1.194)^5 \] ### Step 4: Solving for the Annual Percentage Rate The future value from the single successful loan must be the FV calculated above. The loan amount is $101,000, so: \[ FV = \$101,000 \times (1 + r)^5 \] Set this equal to the required FV: \[ \$101,000 \times (1 + r)^5 = \$1,010,000 \times (1.194)^5 \] \[ (1 + r)^5 = \frac{\$1,010,000 \times (1.194)^5}{\$101,000} \] \[ (1 + r)^5 = 10 \times (1.194)^5 \] \[ (1 + r)^5 = 10 \times 2.4202 \] \[ (1 + r)^5 = 24.202 \] Now take the 5th root: \[ 1 + r = (24.202)^{1/5} \] \[ 1 + r = 1.8897 \] \[ r = 1.8897 - 1 = 0.8897 \] So the annual percentage rate is: \[ \boxed{88.97\%} \] **Rounded to four decimal places:** \[ \boxed{88.9700\%} \] --- **Final answer:** **88.9700%** (rounded to four decimal places)