You need a loan of ​$120 comma 000 to buy a home. Calculate your monthly payments and total closing costs for each choice below. Briefly discuss how you would decide between the two choices.
Choice​ 1: 30​-year fixed rate at 4​% with closing costs of ​$2700 and no points.
Choice​ 2: 30​-year fixed rate at 3.5​% with closing costs of ​$2700 and 4 points.


To analyze which choice is more financially favorable, we’ll calculate the monthly payments and total closing costs for each mortgage option. Here’s how we can approach the problem:

### 1. Monthly Payments
The formula for calculating monthly mortgage payments is:
\[
M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
\]
where:
- $ M $ = monthly payment,
- $ P $ = loan principal (in this case, $120,000),
- $ r $ = monthly interest rate (annual rate divided by 12),
- $ n $ = total number of payments (30 years * 12 months = 360).

#### Choice 1: 30-Year Fixed Rate at 4% (No Points)
1. **Interest Rate:** 4% annually, so the monthly interest rate is $ \frac{0.04}{12} = 0.003333 $.
2. **Monthly Payment Calculation:**
   \[
   M = \frac{120{,}000 \times 0.003333 \times (1 + 0.003333)^{360}}{(1 + 0.003333)^{360} - 1} \approx 572.90
   \]
3. **Closing Costs:** $2,700.

#### Choice 2: 30-Year Fixed Rate at 3.5% with 4 Points
1. **Interest Rate:** 3.5% annually, so the monthly interest rate is $ \frac{0.035}{12} = 0.002917 $.
2. **Monthly Payment Calculation:**
   \[
   M = \frac{120{,}000 \times 0.002917 \times (1 + 0.002917)^{360}}{(1 + 0.002917)^{360} - 1} \approx 538.58
   \]
3. **Closing Costs:** $2,700 + (4 points, or 4% of $120,000) = $2,700 + $4,800 = $7,500.

### Summary
| Choice            | Monthly Payment | Closing Costs |
|-------------------|-----------------|---------------|
| **Choice 1**      | $572.90         | $2,700       |
| **Choice 2**      | $538.58         | $7,500       |

### Total Loan Cost Comparison (over 30 years)
1. **Choice 1 Total Cost:** $ (572.90 \times 360) + 2,700 = 206,244 + 2,700 = 208,944 $.
2. **Choice 2 Total Cost:** $ (538.58 \times 360) + 7,500 = 193,888.80 + 7,500 = 201,388.80 $.

### Decision
Although Choice 2 has higher closing costs upfront, it ultimately leads to lower monthly payments and a lower total cost over the 30-year period, making it the more economical choice in the long run. However, if you prefer lower initial costs and are unsure if you’ll stay in the home long-term, Choice 1 might be more suitable.

Would you like more detailed calculations or have any questions?

---

1. How would the break-even point affect choosing between the options?
2. What are points, and how do they influence loan terms?
3. How would the total cost change with a shorter loan term?
4. How would changes in interest rates affect each choice?
5. What if the down payment or loan amount were different?

**Tip:** Paying points lowers your interest rate, which can reduce total costs if you plan to stay in the home long-term.

You need a loan of $120,000 to buy a home. Calculate your monthly payments and total closing costs for each choice below. Briefly discuss how you would decide between the two choices.

Choice​ 1: 30​-year fixed rate at 4​% with closing costs of ​$2700 and no points.

Choice​ 2: 30​-year fixed rate at 3.5​% with closing costs of ​$2700 and 4 points.

Learn how to compare two 30-year fixed-rate mortgage options for a $120,000 loan, with monthly payment and closing cost calculations. Choice 1 has a 4% rate with $2,700 closing costs; Choice 2 offers 3.5% with $7,500 closing costs. Ideal for students in Grades 11-12 covering financial math concepts.

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