Suppose you take out a $185,000 mortgage for 30 years at 5.85% interest.

(a) Find the monthly payment on this mortgage. $

(b) Fill out the first two rows of the amortization schedule below. Round your answers to the nearest dollar.




Payment NumberInterest PaymentPrincipal PaymentBalance of Loan

1

$

$

$

2

$

$

To solve this problem, we need to break it down into two parts:

### Part (a): Finding the Monthly Payment

The monthly payment for a mortgage can be calculated using the formula for a fixed-rate mortgage:

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

Where:
- $ M $ is the monthly mortgage payment.
- $ P $ is the loan principal (in this case, $185,000).
- $ r $ is the monthly interest rate, which is the annual interest rate divided by 12. (5.85% annual interest = 0.0585 / 12).
- $ n $ is the number of total payments (for a 30-year mortgage, this is $ 30 \times 12 = 360 $).

### Part (b): Filling Out the First Two Rows of the Amortization Schedule

An amortization schedule shows how each mortgage payment is split between paying interest and paying down the principal. For each payment, the interest portion is calculated as:

\[
\text{Interest Payment} = \text{Loan Balance} \times \text{Monthly Interest Rate}
\]

The principal payment is then:

\[
\text{Principal Payment} = \text{Total Monthly Payment} - \text{Interest Payment}
\]

The new balance after each payment is:

\[
\text{New Balance} = \text{Old Balance} - \text{Principal Payment}
\]

Let me calculate both parts for you.### Part (a): Monthly Payment
The monthly mortgage payment is approximately **$1,091.39**.

### Part (b): Amortization Schedule (First Two Payments)

| Payment Number | Interest Payment | Principal Payment | Balance of Loan |
|----------------|------------------|-------------------|-----------------|
| 1              | $902             | $190              | $184,810        |
| 2              | $901             | $190              | $184,620        |

Would you like more details on how these values were calculated or help with something else?

---

Here are 5 follow-up questions:
1. What is the total interest paid over the life of the loan?
2. How much of the loan will be paid after 10 years?
3. How does the amortization schedule change with a higher interest rate?
4. What happens if an extra $100 is added to each monthly payment?
5. How is the monthly payment affected by a shorter loan term (e.g., 15 years)?

**Tip:** Making extra payments early in the loan can significantly reduce the total interest paid.

Suppose you take out a $185,000 mortgage for 30 years at 5.85% interest.

(a) Find the monthly payment on this mortgage. $

(b) Fill out the first two rows of the amortization schedule below. Round your answers to the nearest dollar.

Payment Number Interest Payment Principal Payment Balance of Loan
1
$
$
$
2
$
$

Learn how to calculate the monthly payment and fill out the first two rows of the amortization schedule for a $185,000 mortgage with a 5.85% interest rate over 30 years. Understand mortgage payment formulas and amortization breakdown with detailed steps and examples.

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