If you finance $50,000 of the purchase of your new home at 4.40% compounded monthly for 30 years, the monthly payment will be $250.38.
If instead your had a rate of 4.80% compounded monthly for 15 years, the monthly payment will be $390.21. How much do you pay in total for the $50,000 mortgage if you finance it for 30 years?
Total payment = ?
How much do you save (in total payments) if you finance for 15 years instead? ? dollars
$50000 @ 4.40% for 30 yrs.
Pt = $250.38/mo * 360mo = $90136.80
$50000 @ 4.80% for 15yrs.
Pt = $390.21/mo * 180mo = $70237.80.
Save: $90136.80 - 70237.80 = $19,899.
To calculate the total payment for the $50,000 mortgage over 30 years, we can use the formula for the monthly payment of a fixed-rate mortgage:
Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Principal amount (loan amount) = $50,000
r = Monthly interest rate = 4.40% / 100 / 12 = 0.0036667
n = Total number of monthly payments = 30 years * 12 months = 360 months
Plugging these values into the formula, we get:
Monthly payment = $50,000 * 0.0036667 * (1 + 0.0036667)^360 / ((1 + 0.0036667)^360 - 1) = $250.38
The monthly payment for a 30-year mortgage is $250.38.
To calculate the total payment over 30 years, we multiply the monthly payment by the total number of monthly payments:
Total payment = Monthly payment * Total number of monthly payments
Total payment = $250.38 * 360 = $90,136.80
Therefore, the total payment for the $50,000 mortgage over 30 years is $90,136.80.
To calculate the savings in total payments when financing for 15 years instead of 30 years, we can subtract the total payment for the 15-year mortgage from the total payment for the 30-year mortgage:
Savings = Total payment (30 years) - Total payment (15 years)
Savings = $90,136.80 - (15 years * 12 months * $390.21)
Savings = $90,136.80 - $70,237.80
Savings = $19,899.00
Therefore, you would save $19,899.00 in total payments if you finance the $50,000 mortgage for 15 years instead of 30 years.