For a 30-year house mortgage of $375,000 at 5.8% interest, find the following. (Round your final answers to two decimal places.)
(a) the amount of the first monthly payment that goes to repay principal
$ 


(b) the amount of the 121st month's payment (after 10 years) that goes toward payment of principal
$ 
 

To solve this mortgage problem, we will use the formula for the monthly mortgage payment and the amortization process.

### Step 1: Calculate the monthly mortgage payment.
The monthly payment $ M $ for a fixed-rate mortgage is calculated using the formula:

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

Where:
- $ P $ is the loan amount, $ P = 375,000 $
- $ r $ is the monthly interest rate, $ r = \frac{5.8\%}{12} = \frac{0.058}{12} $
- $ n $ is the total number of payments, $ n = 30 \times 12 = 360 $ (for a 30-year mortgage)

We will first calculate the monthly payment $ M $.

### Step 2: Determine how much of the first payment goes toward the principal.
The principal payment in any given month is the difference between the total monthly payment $ M $ and the interest for that month. For the first month:
- The interest payment is $ P \times r $.

### Step 3: Determine how much of the 121st payment (after 10 years) goes toward the principal.
By the 121st payment, the remaining loan balance needs to be determined. We'll calculate it using the amortization formula for the remaining balance, and then calculate the interest and principal portion for that month.

Let me calculate these values for you.Here are the results:

(a) The amount of the first monthly payment that goes to repay the principal is **$387.82**.

(b) The amount of the 121st month's payment (after 10 years) that goes toward the payment of the principal is **$2,203.67**.

Would you like more details or have any other questions?

Here are 5 related questions to consider:
1. How does increasing the interest rate affect the monthly payment?
2. What happens to the principal portion of the payment over time?
3. How would a 15-year mortgage change the principal repayment structure?
4. How much total interest is paid over the life of the mortgage?
5. What impact does making extra payments on the mortgage have?

**Tip:** Early in a mortgage, most of the payment goes toward interest. Over time, more of the payment goes toward repaying the principal.

For a 30-year house mortgage of $375,000 at 5.8% interest, find the following: (a) the amount of the first monthly payment that goes to repay principal, (b) the amount of the 121st month's payment (after 10 years) that goes toward payment of principal.

Find out how to calculate the principal repayment for a 30-year mortgage of $375,000 at 5.8% interest. This problem walks you through the monthly payment formula, how much goes toward the principal in the first and 121st payments, and amortization concepts. Suitable for college-level students.

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