You have an amortized home loan for
30
30​ years at
3.8
3.8
%
%​ and a home that is selling for
$
335
,
000.00
$335,000.00.

a) How much will you put down if you make a
15
%
15%​ down payment? Round to the nearest cent.
$
$
Preview

b) How much will you have to borrow with a
15
%
15%​ down payment? Round to the nearest cent.
$
$
Preview

c) What will your monthly mortgage payments be? Round to the nearest cent.
$
$
Preview

d) How much will you pay in total for the home (loan + down)? Round to the nearest cent.
$
$
Preview

e) How much interest will you pay in total? Round to the nearest cent.
$
$
Preview

Let's break down each part of the problem.

### a) Down Payment Calculation
The down payment is calculated as a percentage of the selling price of the home.

\[
\text{Down Payment} = \text{Selling Price} \times \frac{\text{Down Payment Percentage}}{100}
\]

Given:
- Selling Price = \$335,000.00
- Down Payment Percentage = 15%

\[
\text{Down Payment} = 335,000 \times \frac{15}{100} = 335,000 \times 0.15 = 50,250.00
\]

So, the down payment is **\$50,250.00**.

### b) Loan Amount Calculation
The loan amount is the selling price minus the down payment.

\[
\text{Loan Amount} = \text{Selling Price} - \text{Down Payment}
\]

\[
\text{Loan Amount} = 335,000 - 50,250 = 284,750.00
\]

So, the loan amount is **\$284,750.00**.

### c) Monthly Mortgage Payment Calculation
The monthly mortgage payment can be calculated using the formula for a fixed-rate mortgage:

\[
M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $ M $ = Monthly mortgage payment
- $ P $ = Loan amount = \$284,750.00
- $ r $ = Monthly interest rate = Annual interest rate / 12 = $ \frac{3.8\%}{12} = 0.003167 $
- $ n $ = Total number of payments = Loan term in years × 12 = $ 30 \times 12 = 360 $ payments

Let's calculate:

\[
M = 284,750 \times \frac{0.003167(1 + 0.003167)^{360}}{(1 + 0.003167)^{360} - 1}
\]

I'll calculate this value.

\[
M \approx 1,330.67
\]

So, the monthly mortgage payment is **\$1,330.67**.

### d) Total Payment for the Home
The total payment for the home is the sum of the total loan payments and the down payment.

Total loan payments = Monthly mortgage payment × Number of payments

\[
\text{Total Loan Payments} = 1,330.67 \times 360 = 479,041.20
\]
\[
\text{Total Payment for the Home} = \text{Total Loan Payments} + \text{Down Payment} = 479,041.20 + 50,250 = 529,291.20
\]

So, the total payment for the home is **\$529,291.20**.

### e) Total Interest Paid
The total interest paid is the total loan payments minus the original loan amount.

\[
\text{Total Interest Paid} = \text{Total Loan Payments} - \text{Loan Amount}
\]
\[
\text{Total Interest Paid} = 479,041.20 - 284,750 = 194,291.20
\]

So, the total interest paid is **\$194,291.20**.

### Summary of Answers:
a) Down Payment: **\$50,250.00**  
b) Loan Amount: **\$284,750.00**  
c) Monthly Mortgage Payment: **\$1,330.67**  
d) Total Payment for the Home: **\$529,291.20**  
e) Total Interest Paid: **\$194,291.20**

Do you want more details or have any questions? Here are some related questions to consider:

1. How would the mortgage payment change if the interest rate increased by 0.5%?
2. What would the total interest paid be with a 20% down payment instead?
3. How does the length of the loan term affect the total interest paid?
4. What is the impact of paying an additional \$100 per month on the mortgage?
5. How would the loan change if the selling price was \$350,000 instead?

**Tip:** Making extra payments on your mortgage can significantly reduce the amount of interest you pay over the life of the loan.

Learn how to calculate an amortized home loan with a 15% down payment. Explore calculations for the down payment, loan amount, monthly mortgage payments, total payment for the home, and total interest paid. Get detailed solutions and round to the nearest cent.

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