Harriet Marcus is concerned about the financing of a home. She saw a small cottage that sells for $51,000. Assuming that she puts 20% down, what will be her monthly payment and the total cost of interest over the cost of the loan for each assumption? (Use the Table 15.1)

Note: Do not round intermediate calculations. Round your answers to the nearest cent.
Monthly payment	Total cost of interest
a. 25 Years, 3.25% chart says 4.87316
b. 25 Years, 3.75%		chart says 5.14131
c. 25 Years, 4.00%		chart says 5.27837
d. 25 Years, 4.25%		chart says 5.41738

Let's break down the problem into several parts to determine both the monthly payment and the total cost of interest for each case.

### Step 1: Determine the loan amount.
Harriet is putting 20% down on the $51,000 cottage, so she will be financing 80% of the purchase price.

\[
\text{Loan amount} = 51,000 \times (1 - 0.20) = 51,000 \times 0.80 = 40,800
\]

### Step 2: Calculate the monthly payment using the provided factors from the table.

For a 25-year loan, the formula to calculate the monthly payment is:

\[
\text{Monthly Payment} = \frac{\text{Loan amount}}{1,000} \times \text{Factor}
\]

Where:
- Loan amount is the amount financed ($40,800)
- Factor is the corresponding value from Table 15.1 for the interest rate and loan period

### Step 3: Calculate the total cost of interest.

The total cost of the loan is the monthly payment multiplied by the total number of payments (number of months = 25 years × 12 months per year = 300 months). The total cost of interest is the total cost of the loan minus the loan amount.

\[
\text{Total cost of interest} = \text{(Monthly payment} \times \text{300)} - \text{Loan amount}
\]

Now, let's calculate this for each case:

---

### a) 25 Years, 3.25%, Factor = 4.87316

**Monthly Payment:**
\[
\text{Monthly Payment} = \frac{40,800}{1,000} \times 4.87316 = 40.8 \times 4.87316 = 198.47
\]

**Total Cost of Interest:**
\[
\text{Total cost of interest} = (198.47 \times 300) - 40,800 = 59,541 - 40,800 = 18,741
\]

---

### b) 25 Years, 3.75%, Factor = 5.14131

**Monthly Payment:**
\[
\text{Monthly Payment} = \frac{40,800}{1,000} \times 5.14131 = 40.8 \times 5.14131 = 209.77
\]

**Total Cost of Interest:**
\[
\text{Total cost of interest} = (209.77 \times 300) - 40,800 = 62,931 - 40,800 = 22,131
\]

---

### c) 25 Years, 4.00%, Factor = 5.27837

**Monthly Payment:**
\[
\text{Monthly Payment} = \frac{40,800}{1,000} \times 5.27837 = 40.8 \times 5.27837 = 215.36
\]

**Total Cost of Interest:**
\[
\text{Total cost of interest} = (215.36 \times 300) - 40,800 = 64,608 - 40,800 = 23,808
\]

---

### d) 25 Years, 4.25%, Factor = 5.41738

**Monthly Payment:**
\[
\text{Monthly Payment} = \frac{40,800}{1,000} \times 5.41738 = 40.8 \times 5.41738 = 221.02
\]

**Total Cost of Interest:**
\[
\text{Total cost of interest} = (221.02 \times 300) - 40,800 = 66,306 - 40,800 = 25,506
\]

---

### Summary of Results:

| Interest Rate | Monthly Payment | Total Cost of Interest |
|---------------|-----------------|------------------------|
| 3.25%         | $198.47         | $18,741                |
| 3.75%         | $209.77         | $22,131                |
| 4.00%         | $215.36         | $23,808                |
| 4.25%         | $221.02         | $25,506                |

Would you like further clarification on any of these calculations or additional details?

### 5 Related Questions:
1. How would the results change if Harriet put down a different percentage, such as 15%?
2. How would the total cost of interest be affected if the loan term was shortened to 20 years?
3. What is the impact of a higher interest rate on the overall cost of a loan?
4. Can Harriet reduce the total cost of interest by making extra monthly payments?
5. What would happen to her monthly payment if the interest rate drops to 3%?

### Tip:
Making additional payments on a mortgage can significantly reduce the total interest paid over the life of the loan.

Harriet Marcus is concerned about the financing of a home. She saw a small cottage that sells for $51,000. Assuming that she puts 20% down, what will be her monthly payment and the total cost of interest over the cost of the loan for each assumption? (Use the Table 15.1)

Calculate monthly mortgage payments and total cost of interest for a $51,000 home, assuming a 20% down payment. Explore loan terms over 25 years at different interest rates: 3.25%, 3.75%, 4.00%, and 4.25%. Understand how to compute loan amounts, payments, and interest using key formulas. Ideal for high school students and anyone learning about mortgage financing.

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