Question

Consider a home mortgage of $225,000 at a fixed APR of 6% for 30 years. Calculate the monthly payment.

Answer 1

$1,348.99

Explanation:

To calculate the monthly mortgage payment for a fixed-rate mortgage, use the formula for a fixed monthly payment on a loan.

Monthly Payment Formula

`\boxed{PMT=(Pr\left(1+r\right)^n)/(\left(1+r\right)^n-1)}`

where:

• PMT = Monthly payment.
• P = Loan amount.
• r = Interest rate per month (in decimal form).
• n = Term of the loan (in months).

In this case:

• P = $225,000
• r = 6%/12 = 0.06/12 = 0.005
• n = 30 × 12 = 360 months

Substitute the values into the formula and solve for PMT:

`PMT=(225000 \cdot 0.005\left(1+0.005\right)^(360))/(\left(1+0.005\right)^(360)-1)`

`PMT=(1125\left(1.005\right)^(360))/(\left(1.005\right)^(360)-1)`

`PMT=1348.98868...`

So, the monthly mortgage payment for a $225,000 loan with a fixed APR of 6% for 30 years is approximately $1,348.99.