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A family borrowed $72,000 to buy a house. The loan was at 6.2% and for 25 years. The monthly payments were $472.74 each.

(a) How much of the first month's payment was interest, and how much was principal?

interest

$

principal

$

(b) What was the total amount paid over the 25 years?

Let's break down the problem step by step:

### (a) How much of the first month's payment was interest, and how much was principal?

The formula for monthly interest is:

\[
\text{Interest for the first month} = P \times \frac{r}{12}
\]

Where:
- $ P $ is the loan amount (principal) = \$72,000
- $ r $ is the annual interest rate = 6.2% = 0.062

Substitute these values into the formula:

\[
\text{Interest for the first month} = 72,000 \times \frac{0.062}{12}
\]

Let's calculate the interest:

\[
\text{Interest for the first month} = 72,000 \times 0.0051667
\]

The principal payment for the first month is the remainder of the total monthly payment after subtracting the interest:

\[
\text{Principal payment} = \text{Monthly payment} - \text{Interest for the first month}
\]

Where:
- Monthly payment = \$472.74

Now, I'll compute the exact values.For the first month's payment:
- Interest: **$372.00**
- Principal: **$100.74**

### (b) What was the total amount paid over 25 years?

The total amount paid over the full term is calculated by multiplying the monthly payment by the total number of months:

\[
\text{Total amount paid} = \text{Monthly payment} \times \text{Number of months}
\]

Where:
- $ \text{Number of months} = 25 \times 12 = 300 $

Let's calculate the total amount paid.The total amount paid over 25 years is **$141,822.00**.

### Summary:
- (a) First month's interest: **$372.00** and principal: **$100.74**
- (b) Total amount paid over 25 years: **$141,822.00**

Would you like any additional details or have questions?

Here are some related questions for further exploration:
1. How much total interest was paid over the 25 years?
2. How would the total payment change if the interest rate was 5% instead?
3. How long would it take to pay off the loan if the monthly payment increased by 10%?
4. What if the loan was for 30 years instead of 25 years—how much would the total payment be?
5. What is the outstanding balance after the first year of payments?

**Tip:** The earlier you pay more towards the principal, the less overall interest you'll end up paying!

A family borrowed $72,000 to buy a house. The loan was at 6.2% and for 25 years. The monthly payments were $472.74 each.
(a) How much of the first month's payment was interest, and how much was principal?
(b) What was the total amount paid over the 25 years?

Explore the breakdown of a $72,000 home loan at 6.2% over 25 years. Calculate how much of the first month's payment is interest and principal. Discover the total amount paid over the loan's lifetime, with detailed formulas and steps. Suitable for students in Grades 10-12.

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