Question

Suppose I take out a mortgage on a $300,000 home and pay 20% of home’s value for a down payment. It is a 30-year mortgage with a fixed interest rate of 5%. Make sure to explain how you got your answers to the following and/or include a screenshot from Desmos or your calculator so I can see how you got your answer.

Answer 1

Certainly! To calculate the monthly mortgage payment for a $300,000 home with a 20% down payment and a 30-year fixed interest rate of 5%, you can use the formula for the monthly payment of a fixed-rate mortgage:

M = P[r(1 + r)^n] / [(1 + r)^n - 1]

Where:
M = Monthly Payment
P = Principal Loan Amount (Original Loan Amount minus Down Payment)
r = Monthly Interest Rate (Annual Interest Rate divided by 12 months)
n = Total Number of Payments (Loan Term in years multiplied by 12 months)

First, calculate the principal loan amount (P):

P = Home Value - Down Payment
P = $300,000 - (20% of $300,000)
P = $300,000 - $60,000
P = $240,000

Next, calculate the monthly interest rate (r):

r = Annual Interest Rate / 12 months
r = 5% / 12
r = 0.05 / 12
r = 0.0041667 (approximately)

Now, calculate the total number of payments (n):

n = Loan Term in Years * 12 months
n = 30 years * 12
n = 360 months

Now, plug these values into the formula:

M = $240,000 * [0.0041667(1 + 0.0041667)^360] / [(1 + 0.0041667)^360 - 1]

Using a calculator, you can compute this monthly payment, which should be approximately $1,288.37.

So, the estimated monthly mortgage payment for a $300,000 home with a 20% down payment and a 30-year fixed interest rate of 5% is about $1,288.37.