Find the monthly payment needed to amortize a typical $205,000 mortgage loan amortized over 30 years at an annual interest rate of 5.9% compounded monthly. (Round your answers to the nearest cent.)
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To find the monthly payment on a mortgage, we can use the formula for the monthly payment of a loan amortized over a fixed period of time:

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

Where:
- $M$ = monthly payment
- $P$ = loan principal ($205,000)
- $r$ = monthly interest rate (annual rate / 12)
- $n$ = total number of payments (loan term in years × 12 months)

### Step 1: Calculate monthly interest rate
The annual interest rate is 5.9%, so the monthly interest rate is:
\[
r = \frac{5.9\%}{12} = \frac{0.059}{12} = 0.00491667
\]

### Step 2: Calculate the total number of payments
For a 30-year mortgage, the total number of payments is:
\[
n = 30 \times 12 = 360
\]

### Step 3: Plug values into the formula
Now, substituting the values into the formula:

\[
M = 205,000 \times \frac{0.004

Find the monthly payment needed to amortize a typical $205,000 mortgage loan amortized over 30 years at an annual interest rate of 5.9% compounded monthly. (Round your answers to the nearest cent.)

Discover how to calculate the monthly payment needed to amortize a $205,000 mortgage over 30 years with a 5.9% annual interest rate compounded monthly. Step-by-step explanation of amortization formulas and concepts for high school students in Grades 10-12.

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