$305,500 with 20% down and finance the remainder of the purchase.compare two mortgage options. 10 years at 3.5% or 15 years at 5%. What’s is the monthly payment and total interest cost for both the 10 and 15 year mortgages. What’s the difference in interest paid between the two options. Round to the nearest cent?

Let's break down this mortgage problem step by step. You are buying a house for $305,500, putting 20% down, and comparing two financing options. We'll calculate:

1. The loan amount after the down payment.
2. The monthly payments for both the 10-year and 15-year mortgage options.
3. The total interest paid for both options.
4. The difference in interest paid between the two options.

### Step 1: Calculate the Loan Amount
You are putting 20% down on the house, so:
\[
\text{Down Payment} = 305,500 \times 0.20 = 61,100
\]
The loan amount is then:
\[
\text{Loan Amount} = 305,500 - 61,100 = 244,400
\]

### Step 2: Calculate the Monthly Payments
The formula to calculate the monthly mortgage payment is:
\[
M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]
Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount ($244,400).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the number of monthly payments (loan term in years multiplied by 12).

#### 10-Year Mortgage at 3.5%
- $ r = \frac{3.5\%}{12} = 0.002917 $
- $ n = 10 \times 12 = 120 $ months

Plugging these into the formula:
\[
M_{10} = 244,400 \times \frac{0.002917(1+0.002917)^{120}}{(1+0.002917)^{120} - 1} = 2,416.04
\]

#### 15-Year Mortgage at 5%
- $ r = \frac{5\%}{12} = 0.004167 $
- $ n = 15 \times 12 = 180 $ months

Plugging these into the formula:
\[
M_{15} = 244,400 \times \frac{0.004167(1+0.004167)^{180}}{(1+0.004167)^{180} - 1} = 1,929.18
\]

### Step 3: Calculate the Total Interest Paid
The total interest paid is the difference between the total amount paid (monthly payment × number of payments) and the loan amount.

#### 10-Year Mortgage
\[
\text{Total Paid} = 2,416.04 \times 120 = 289,924.80
\]
\[
\text{Total Interest (10-year)} = 289,924.80 - 244,400 = 45,524.80
\]

#### 15-Year Mortgage
\[
\text{Total Paid} = 1,929.18 \times 180 = 347,252.40
\]
\[
\text{Total Interest (15-year)} = 347,252.40 - 244,400 = 102,852.40
\]

### Step 4: Difference in Interest Paid
\[
\text{Difference in Interest} = 102,852.40 - 45,524.80 = 57,327.60
\]

### Summary
- **Monthly Payment (10-year, 3.5%)**: $2,416.04
- **Monthly Payment (15-year, 5%)**: $1,929.18
- **Total Interest (10-year)**: $45,524.80
- **Total Interest (15-year)**: $102,852.40
- **Difference in Interest**: $57,327.60

Would you like more details or explanations? Here are some related questions:

1. How does the down payment affect the loan amount?
2. What would happen if the interest rate for the 15-year loan dropped by 1%?
3. How would paying extra principal monthly affect the interest paid?
4. What are the benefits of a shorter mortgage term despite higher monthly payments?
5. How does compound interest impact long-term mortgage interest?

**Tip**: Choosing a shorter-term mortgage can save you significant interest, but the higher monthly payments may affect your budget flexibility.

$305,500 with 20% down and finance the remainder of the purchase. Compare two mortgage options: 10 years at 3.5% or 15 years at 5%. What’s the monthly payment and total interest cost for both the 10- and 15-year mortgages? What’s the difference in interest paid between the two options?

Compare a $305,500 mortgage with 20% down for two loan options: 10 years at 3.5% or 15 years at 5%. Find the monthly payment for each option, calculate the total interest paid, and discover the difference in interest between the two choices. Learn about amortization and interest rate impacts on loan costs. Suitable for students in Grades 11-12 or those studying finance.

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