You are thinking of purchasing a house. The house costs $322,000. You have $60,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 20-year mortgage that requires annual payments and has an interest rate of 9% per year. What will be your annual payment if you sign this mortgage?

The annual payment will be $

(Round to the nearest cent.)

To calculate the annual payment for a mortgage, we can use the **amortization formula**:

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

Where:
- $A$ = annual payment
- $P$ = loan amount (the house price minus the down payment)
- $r$ = annual interest rate (expressed as a decimal)
- $n$ = number of payments (years)

### Step 1: Calculate the loan amount.
\[
P = \text{House Price} - \text{Down Payment} = 322,000 - 60,000 = 262,000
\]

### Step 2: Convert the interest rate.
\[
r = \frac{9}{100} = 0.09
\]

### Step 3: Use the formula with $n = 20$ years and $r = 0.09$.

Now let's calculate the annual payment.The annual payment for the mortgage would be **$28,701.18**, rounded to the nearest cent.

Would you like further details on how this was calculated or have any additional questions?

Here are five related questions for further exploration:
1. How does the payment change with a different interest rate, like 7%?
2. What would be the total interest paid over the life of the mortgage?
3. How much would you save on interest if the mortgage term was 15 years instead of 20?
4. What happens if you increase the down payment by $10,000?
5. How does a bi-weekly payment plan affect the total interest paid?

**Tip:** The larger your down payment, the less you'll need to borrow, reducing both your annual payments and total interest paid over the mortgage term.

You are thinking of purchasing a house. The house costs $322,000. You have $60,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 20-year mortgage that requires annual payments and has an interest rate of 9% per year. What will be your annual payment if you sign this mortgage?

Learn how to calculate the annual mortgage payment for a $322,000 house with a $60,000 down payment. This step-by-step guide covers key financial concepts such as amortization and interest rate calculations using a 20-year mortgage term and 9% interest rate. Suitable for college-level finance and business mathematics students.

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