Paying 13 mortgage payments instead of 12 per year can save you thousands in interest cost. If you had a $175,000 mortgage at 6% for 30 years, how much extra would you have to pay per year to make 13 instead of 12 mortgage payments per year? How much would you pay if you paid 1/12 of it per month?
To calculate how much extra you would have to pay per year to make 13 instead of 12 mortgage payments per year, first, we need to calculate the amount of the monthly mortgage payment. We can use the loan amount ($175,000), the interest rate (6%), and the mortgage term (30 years) to determine the monthly payment.
Using the formula for calculating a fixed monthly mortgage payment:
Monthly interest rate = Annual interest rate / 12 months = 6% / 12 = 0.5%
Number of monthly payments = Mortgage term in years * 12 months = 30 * 12 = 360 months
Now, using the formula:
Monthly mortgage payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Loan principal (mortgage amount)
r = Monthly interest rate
n = Number of monthly payments
Plugging in the values:
r = 0.5% = 0.005
n = 360
P = $175,000
Monthly payment = 175,000 * (0.005 * (1 + 0.005)^360) / ((1 + 0.005)^360 - 1)
= $1,049.31
Now, to calculate the extra amount you need to pay per year to make 13 instead of 12 mortgage payments, we can multiply the monthly payment by 12/13:
Extra payment per year = Monthly payment * (12/13)
= $1,049.31 * (12/13)
≈ $968.41
Therefore, you would need to pay an extra $968.41 per year to make 13 instead of 12 mortgage payments.
Next, if you pay 1/12 of the mortgage amount per month, the monthly payment would be equal to the mortgage amount divided by 12:
Monthly payment = $175,000 / 12
= $14,583.33
Therefore, you would have to pay $14,583.33 per month if you choose to pay 1/12 of the mortgage amount each month.