Question: User: $180,000 is financed for 20 years at 5.25% APR monthly mortgage payment
1. **State the problem:** Calculate the monthly mortgage payment for a loan of $180000$ financed over $20$ years at an annual percentage rate (APR) of $5.25\%$.
2. **Formula used:** The monthly mortgage payment $M$ is given by the formula:
$$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$
where:
- $P$ is the loan principal ($180000$),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of payments (years times 12).
3. **Calculate monthly interest rate:**
$$r = \frac{5.25}{100 \times 12} = \frac{5.25}{1200} = 0.004375$$
4. **Calculate total number of payments:**
$$n = 20 \times 12 = 240$$
5. **Substitute values into the formula:**
$$M = 180000 \times \frac{0.004375(1+0.004375)^{240}}{(1+0.004375)^{240} - 1}$$
6. **Calculate $(1+r)^n$:**
$$ (1+0.004375)^{240} = 1.004375^{240} \approx 2.8577 $$
7. **Calculate numerator:**
$$0.004375 \times 2.8577 = 0.0125$$
8. **Calculate denominator:**
$$2.8577 - 1 = 1.8577$$
9. **Calculate fraction:**
$$\frac{0.0125}{1.8577} \approx 0.00673$$
10. **Calculate monthly payment:**
$$M = 180000 \times 0.00673 = 1211.40$$
**Final answer:** The monthly mortgage payment is approximately $1211.40$.