Mortgage Discount Points Calculator

What is a Mortgage Discount Points Calculator?

A Mortgage Discount Points Calculator is a financial tool that helps borrowers estimate the potential savings from buying mortgage points. Mortgage points, also known as discount points, are fees paid directly to the lender at closing in exchange for a reduced interest rate. This calculator helps you determine if paying for points is a good financial decision based on how long you plan to stay in your home.

Formula for Mortgage Discount Points Calculation

The calculation involves several steps:

1. Cost of Points: \(C_p = L \times \frac{P}{100}\)
2. New Interest Rate: \(r_{new} = r - (P \times 0.25)\)
3. Monthly Payment: \(M = L \times \frac{r_m(1+r_m)^n}{(1+r_m)^n-1}\)

Where:

• \(C_p\) = Cost of Points
• \(L\) = Loan Amount
• \(P\) = Number of Points
• \(r\) = Annual Interest Rate (as a decimal)
• \(r_{new}\) = New Annual Interest Rate (as a decimal)
• \(r_m\) = Monthly Interest Rate (as a decimal)
• \(n\) = Total Number of Payments
• \(M\) = Monthly Payment

Calculation Steps

1. Calculate the cost of points
2. Determine the new interest rate after applying points
3. Calculate monthly payments for both the original and new interest rates
4. Compute monthly savings
5. Determine the break-even point

Example

Let's consider a scenario with the following details:

• Loan Amount: $300,000
• Original Interest Rate: 4.5% per year
• Loan Term: 30 years
• Points: 2

Calculation:

1. Cost of points: $300,000 × (2/100) = $6,000
2. New interest rate: 4.5% - (2 × 0.25%) = 4%
3. Original monthly payment: $1,520.06
4. New monthly payment: $1,432.25
5. Monthly savings: $1,520.06 - $1,432.25 = $87.81
6. Break-even point: $6,000 / $87.81 ≈ 68 months

In this example, buying points would save the borrower $87.81 per month. The break-even point is about 68 months (5.67 years). If the borrower plans to keep the mortgage longer than this, buying points could be beneficial.