Mortgage company lets you pay a point (1% of total amount of loan)to reduce APR from 6.5% to 6.25% on a $400,000
30-yr mortgage with monthly payments.
Plan to be in house for at least five years.
Should you pay the point?
No
To determine whether you should pay the point to reduce the APR, we'll need to compare the cost of paying the point with the potential savings on interest over the five-year period.
Step 1: Calculate the cost of paying the point:
1% of $400,000 = $4,000
Step 2: Calculate the potential interest savings:
First, determine the monthly payment on the original loan:
Using an online mortgage calculator or a financial calculator, you can calculate the monthly payment for a 30-year mortgage at 6.5% interest rate on $400,000.
Assuming the interest is compounded monthly:
N = 30 years * 12 months = 360
PV = $400,000
I/Y = 6.5% / 12 (monthly interest rate)
PMT = ? (monthly payment)
Using the PMT function in a financial calculator or an online calculator, you'll find that the monthly payment is approximately $2,517.58.
Next, calculate the total interest paid over five years for the original loan:
Total interest = Monthly payment * (number of payments - loan amount)
Total interest = $2,517.58 * (5 years * 12 months - $400,000)
Total interest = $2,517.58 * (60 months - $400,000)
Total interest = $2,517.58 * ($20,660.80)
Total interest = $51,651.74
Step 3: Calculate the potential interest savings with the reduced APR:
Calculate the new monthly payment with the reduced APR:
Using the same mortgage calculator, calculate the monthly payment for a 30-year mortgage at 6.25% interest rate on $400,000.
Assuming the interest is compounded monthly:
N = 30 years * 12 months = 360
PV = $400,000
I/Y = 6.25% / 12 (monthly interest rate)
PMT = ? (monthly payment)
Using the PMT function, you'll find that the new monthly payment is approximately $2,461.56.
Calculate the total interest paid over five years for the new loan:
Total interest = Monthly payment * (number of payments - loan amount)
Total interest = $2,461.56 * (5 years * 12 months - $400,000)
Total interest = $2,461.56 * (60 months - $400,000)
Total interest = $2,461.56 * ($19,695.60)
Total interest = $48,131.70
Step 4: Compare the potential interest savings:
Interest savings = Total interest with original loan - Total interest with new loan
Interest savings = $51,651.74 - $48,131.70
Interest savings = $3,520.04
Step 5: Compare the interest savings with the cost of paying the point:
Comparing the interest savings of $3,520.04 with the cost of paying the point of $4,000, we can see that the interest savings do not fully offset the cost of the point.
Therefore, based solely on the financial perspective, it may not be beneficial for you to pay the point in this scenario. However, it's important to consider other factors such as your personal financial situation and long-term goals before making a decision.
To determine whether paying a point is worth it, you need to compare the cost of the point to the potential savings in interest over the duration of the mortgage.
1. Calculate the cost of the point: Multiply the loan amount by 1% (0.01). For a $400,000 loan, one point would be $4,000.
2. Calculate the monthly payment for each interest rate:
- For a 6.5% APR: Divide the annual interest rate by 12 (months) and multiply it by the loan amount. Then calculate the monthly payment using a mortgage payment calculator or a formula.
- For a 6.25% APR: Repeat the same process as above.
3. Find the total interest paid over five years for each interest rate: Multiply the monthly payment by 12 (months) and then by 5 (years). Subtract the loan amount from this total to calculate the interest paid.
4. Compare the total interest paid for each interest rate:
- Option without paying a point: Calculate the total interest paid for the 6.5% APR.
- Option with paying a point: Calculate the total interest paid for the 6.25% APR, subtracting the cost of the point from the total interest paid.
5. Determine whether the savings in interest justify the upfront cost of the point. If the savings in interest over five years by paying the point is greater than the cost of the point ($4,000), then it may be worthwhile to pay the point.
Keep in mind that this analysis assumes you will stay in the house for at least five years. If you plan to move before that, you may need to factor in the break-even point at which the savings from the lower interest rate outweigh the upfront cost of the point.