1. **State the problem:** We have a 5-year loan of 2863 at 7% annual interest compounded monthly. We need to find the monthly payment and the remaining balance after 2 years. 2. **Formula for monthly payment:** The monthly payment $M$ for a loan amount $P$ with monthly interest rate $r$ over $n$ months is given by: $$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ where $r = \frac{0.07}{12}$ and $n = 5 \times 12 = 60$ months. 3. **Calculate monthly interest rate:** $$r = \frac{0.07}{12} = 0.0058333$$ 4. **Calculate monthly payment:** $$M = 2863 \times \frac{0.0058333(1+0.0058333)^{60}}{(1+0.0058333)^{60} - 1}$$ Calculate $(1+0.0058333)^{60}$: $$1.0058333^{60} \approx 1.42576$$ So, $$M = 2863 \times \frac{0.0058333 \times 1.42576}{1.42576 - 1} = 2863 \times \frac{0.008317}{0.42576}$$ Simplify fraction: $$\frac{0.008317}{0.42576} \approx 0.01954$$ Therefore, $$M = 2863 \times 0.01954 = 55.95$$ Monthly payment is approximately $55.95$. 5. **Calculate remaining balance after 2 years (24 payments):** Remaining balance formula: $$B = P(1+r)^m - M \times \frac{(1+r)^m - 1}{r}$$ where $m=24$ months paid. Calculate $(1+r)^m$: $$1.0058333^{24} \approx 1.1487$$ Calculate balance: $$B = 2863 \times 1.1487 - 55.95 \times \frac{1.1487 - 1}{0.0058333}$$ Calculate numerator of fraction: $$1.1487 - 1 = 0.1487$$ Calculate fraction: $$\frac{0.1487}{0.0058333} \approx 25.49$$ Calculate second term: $$55.95 \times 25.49 = 1425.5$$ Calculate first term: $$2863 \times 1.1487 = 3288.5$$ Calculate remaining balance: $$B = 3288.5 - 1425.5 = 1863$$ 6. **Final answers:** - Monthly payment is approximately **55.95**. - Remaining balance after 2 years is approximately **1863**.