1. **State the problem:** Pat borrows money from the credit union and repays it monthly over 3 years. We need to find the total amount repaid and verify the repayment percentage. 2. **Calculate total repayment:** Pat pays €443.66 per month for 36 months (3 years). $$\text{Total repayment} = 443.66 \times 36 = 15971.76$$ 3. **Calculate amount borrowed:** Pat buys a car for €32000 and trades in an old car for €20000 allowance. $$\text{Amount borrowed} = 32000 - 20000 = 12000$$ 4. **Calculate repayment as a percentage of amount borrowed:** $$\frac{15971.76}{12000} = 1.33098$$ Multiply by 100 to get percentage: $$1.33098 \times 100 = 133.1\%$$ This confirms the repayment is 133.1% of the borrowed amount. 5. **Compound interest problem:** A sum is invested at rate $r\%$ per annum compounded yearly for 3 years, increasing by 33.1%. 6. **Use compound interest formula:** $$A = P\left(1 + \frac{r}{100}\right)^3$$ Since the value increased by 33.1%, $$\frac{A}{P} = 1.331$$ 7. **Solve for $r$:** $$1.331 = \left(1 + \frac{r}{100}\right)^3$$ Take cube root of both sides: $$\sqrt[3]{1.331} = 1 + \frac{r}{100}$$ Calculate cube root: $$1.1 = 1 + \frac{r}{100}$$ Subtract 1: $$\frac{r}{100} = 0.1$$ Multiply both sides by 100: $$r = 10$$ **Final answer:** The annual compound interest rate $r$ is 10%.