Consider a home mortgage of

​$250 comma 000250,000

at a fixed APR of

66​%

for

2020

years.

a. Calculate the monthly payment.

b. Determine the total amount paid over the term of the loan.

c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.

Question content area bottom

Part 1

a. The monthly payment is

​$enter your response here.

To solve this mortgage problem, we will use the formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $M$ = monthly mortgage payment
- $P$ = loan principal (in this case, $250,000)
- $r$ = monthly interest rate (annual interest rate divided by 12)
- $n$ = total number of payments (number of years multiplied by 12)

Let's break it down step by step.

### Given dataTo solve this mortgage problem, we will use the formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $M$ = monthly mortgage payment
- $P$ = loan principal (in this case, $250,000)
- $r$ = monthly interest rate (annual interest rate divided by 12)
- $n$ = total number of payments (number of years multiplied by 12)

Let's break it down step by step.

### Given 
- Principal $P = 250,000$
- Annual interest rate = 6% or 0.06
- Loan term = 20 years

First, convert the annual interest rate to a monthly interest rate:
\[
r = \frac{0.06}{12} = 0.005
\]

Next, calculate the total number of payments:
\[
n = 20 \times 12 = 240 \text{ payments}
\]

Now, let's calculate the monthly payment using the formula.

I will calculate it now.The monthly mortgage payment is approximately **$1,791.08**.

### Next steps:
b. Let's calculate the total amount paid over the term of the loan. The total amount paid is simply the monthly payment multiplied by the number of payments.

I will calculate that now.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can calculate the total amount paid by multiplying the monthly payment by the total number of payments:

\[
\text{Total amount paid} = 1,791.08 \times 240
\]

Would you like to continue with manual calculations or explore more details?

Here are 5 related questions to further your understanding:
1. How would the monthly payment change if the interest rate increased to 7%?
2. What happens to the total interest paid if the loan term is shortened to 15 years?
3. Can you calculate the amount of interest paid in just the first year?
4. What would be the impact of making additional principal payments every month?
5. How does the monthly payment change with a larger down payment?

**Tip**: Reducing the loan term often increases the monthly payment but can significantly lower the total interest paid over time.

Consider a home mortgage of $250,000 at a fixed APR of 6% for 20 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Learn how to calculate the monthly payment for a $250,000 mortgage at a 6% APR over 20 years. This problem involves the loan amortization formula and provides step-by-step calculations for the total amount paid and interest percentage. Suitable for high school and college students.

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