1. **Problem statement:** Your friend has an equivalent annual rate (EAR) of 4.375% for a 30-year mortgage. You want to borrow 220000 and need to find the monthly payment. 2. **Formula:** The monthly payment $M$ for a loan amount $P$ with monthly interest rate $r$ and total number of payments $n$ is given by: $$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ 3. **Convert EAR to monthly interest rate:** EAR is given by: $$EAR = (1 + r_{monthly})^{12} - 1$$ Rearranged to find $r_{monthly}$: $$r_{monthly} = (1 + EAR)^{\frac{1}{12}} - 1$$ 4. **Calculate monthly interest rate:** $$EAR = 0.04375$$ $$r_{monthly} = (1 + 0.04375)^{\frac{1}{12}} - 1 = 1.04375^{0.083333} - 1$$ Using a calculator: $$r_{monthly} \approx 0.003569$$ 5. **Calculate total number of payments:** $$n = 30 \times 12 = 360$$ 6. **Calculate monthly payment:** $$M = 220000 \times \frac{0.003569(1+0.003569)^{360}}{(1+0.003569)^{360} - 1}$$ Calculate $(1 + r_{monthly})^{360}$: $$1.003569^{360} \approx 3.806$$ 7. **Substitute values:** $$M = 220000 \times \frac{0.003569 \times 3.806}{3.806 - 1} = 220000 \times \frac{0.01358}{2.806}$$ 8. **Simplify fraction:** $$\frac{0.01358}{2.806} \approx 0.004839$$ 9. **Final monthly payment:** $$M = 220000 \times 0.004839 = 1064.58$$ **Answer:** Your monthly payment will be approximately **1064.58**. This means neither 1021.24 nor 1087.95 is correct based on the given EAR and loan amount.