1. **Problem Statement:** We need to find the monthly reduction in fuel cost that will repay the $1300 investment over 5 years with a 12% annual interest rate compounded monthly. 2. **Formula Used:** We use the formula for the present value of an annuity since the monthly savings are like payments that repay the investment: $$PV = PMT \times \frac{1 - (1 + r)^{-n}}{r}$$ where: - $PV = 1300$ (initial investment) - $PMT$ is the monthly reduction in fuel cost (what we want to find) - $r = \frac{0.12}{12} = 0.01$ (monthly interest rate) - $n = 5 \times 12 = 60$ (total number of months) 3. **Rearranging the formula to solve for $PMT$:** $$PMT = PV \times \frac{r}{1 - (1 + r)^{-n}}$$ 4. **Substitute the values:** $$PMT = 1300 \times \frac{0.01}{1 - (1 + 0.01)^{-60}}$$ 5. **Calculate the denominator:** $$1 - (1.01)^{-60} = 1 - \frac{1}{(1.01)^{60}}$$ Calculate $(1.01)^{60}$: $$ (1.01)^{60} \approx 1.8194$$ So, $$1 - \frac{1}{1.8194} = 1 - 0.5495 = 0.4505$$ 6. **Calculate $PMT$:** $$PMT = 1300 \times \frac{0.01}{0.4505} = 1300 \times 0.0222 = 28.86$$ 7. **Interpretation:** The monthly reduction in fuel cost must be approximately $28.86 to repay the $1300 investment with 12% interest compounded monthly over 5 years. **Final answer:** The reduction in monthly fuel cost must be **28.86**.