Suppose you want to buy a house that costs $225,000. You have $45,000 dollars for a down payment. The bank is offering two different mortgage options.
Option A: 30-year mortgage at 4.5%.
Option B: 30-year mortgage at 4.0% with two points. The cost of the points will be rolled into the mortgage.
To calculate the monthly payments for each mortgage option, we can use the mortgage formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = Monthly payment
P = Principal amount (Loan amount)
i = Monthly interest rate
n = Number of monthly payments
Option A:
Loan amount (Principal) = $225,000 - $45,000 = $180,000
Interest rate = 4.5% / 100 = 0.045
Number of monthly payments = 30 years * 12 months/year = 360 months
For Option A:
M = $180,000 [ 0.045(1 + 0.045)^360 ] / [ (1 + 0.045)^360 – 1 ]
Option B:
Loan amount (Principal) = $225,000 - $45,000 = $180,000
Interest rate = 4.0% / 100 = 0.04
Number of monthly payments = 30 years * 12 months/year = 360 months
For Option B:
M = $180,000 [ 0.04(1 + 0.04)^360 ] / [ (1 + 0.04)^360 – 1 ]
However, we need to consider the cost of the points for Option B. "Points" in mortgage terms are a percentage of the loan amount that you pay upfront to receive a lower interest rate. Let's assume each point costs 1% of the loan amount, so for Option B, the cost of the points would be 2% * $180,000 = $3,600.
Thus, the new principal for Option B would be $180,000 + $3,600 = $183,600.
To calculate the monthly payment now for Option B, we use the updated principal amount:
For Option B:
M = $183,600 [ 0.04(1 + 0.04)^360 ] / [ (1 + 0.04)^360 – 1 ]
By calculating the above formulas, you will find the monthly payments for each option.