A couple is buying a house priced at $ 100,000. The couple pays $20,000
down payment up front. If the couple borrows the rest of the money from a
bank at 6 % annual interest rate for the next 20 years, how much will their
payment be at the end of each month?
8


To calculate the monthly payment for the mortgage, we use the **amortization formula**:

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

Where:
- $M$ = Monthly payment
- $P$ = Loan principal (the amount borrowed)
- $r$ = Monthly interest rate (annual interest rate divided by 12)
- $n$ = Total number of payments (loan term in years multiplied by 12)

### Given:
- House price = $100,000
- Down payment = $20,000
- Loan principal $P = 100,000 - 20,000 = 80,000$
- Annual interest rate = 6% or 0.06
- Loan term = 20 years

### Step 1: Find the monthly interest rate:
\[
r = \frac{0.06}{12} = 0.005
\]

### Step 2: Find the total number of payments:
\[
n = 20 \times 12 = 240 \text{ months}
\]

### Step 3: Use the formula to calculate the monthly payment $M$:

\[
M = 80,000 \cdot \frac{0.005(1 + 0.005)^{240}}{(1 + 0.005)^{240} - 1}
\]

Let me calculate this for you.The couple's monthly payment will be approximately **$573.14**.

Would you like further details on how this was calculated, or do you have any other questions?

Here are 5 related questions:
1. What happens to the monthly payment if the interest rate increases?
2. How much interest will the couple pay over the 20-year loan period?
3. What would their monthly payment be if they made a larger down payment?
4. How does paying bi-weekly instead of monthly affect the loan payoff period?
5. Can the couple reduce interest paid by making extra payments each month?

**Tip**: Making extra payments toward the principal reduces the total interest paid over the life of the loan.

A couple is buying a house priced at $100,000. The couple pays $20,000 down payment up front. If the couple borrows the rest of the money from a bank at 6% annual interest rate for the next 20 years, how much will their payment be at the end of each month?

Calculate the monthly mortgage payment for a $100,000 house with a $20,000 down payment and a 6% annual interest rate over 20 years. Learn how to use the amortization formula to find the payment amount, suitable for students in Grades 10-12.

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