Dr. Vance specializes in capital markets and the time value of money, ensuring the complex Break-Even Point (BEP) calculations for discount points are mathematically sound and accurate.
The **Mortgage Points Calculator** helps you analyze the trade-off between paying upfront discount points to lower your interest rate and the time it takes to recoup that cost (Break-Even Point). It solves for **Points Cost ($C_P$)**, **Interest Savings ($I_{saved}$)**, **Break-Even Point (BEP)**, or **Loan Principal ($P$)** based on the other three variables.
Mortgage Points Calculator
*Enter any 3 values to solve for the 4th (P, $R_{orig}$, $R_{new}$, or $C_P$). Loan Term ($T$) must always be entered.
Mortgage Points Formulas & Logic
The core calculation determines the savings on the monthly payment, which is then used to find the Break-Even Point (BEP).
1. Monthly Payment ($M$):
$$ M = P \frac{i(1+i)^n}{(1+i)^n - 1} $$
Where $i$ is the monthly rate and $n$ is the total months ($T \times 12$).
2. Break-Even Point (BEP, in months):
$$ BEP = \frac{\text{Points Cost } (C_P)}{\text{Monthly Savings } (M_{orig} - M_{new})} $$
Formula Source: Investopedia (Mortgage Points)
Variables Explained
- $P$ (Loan Principal): The amount of money being borrowed for the mortgage. (F in input map)
- $R_{orig}$ (Original Rate): The interest rate before purchasing discount points. (P in input map)
- $R_{new}$ (New Rate): The lower interest rate after purchasing discount points. (V in input map)
- $C_P$ (Points Cost): The total dollar cost paid upfront for the points. (Q in input map)
Related Calculators
Analyze other investment and borrowing strategies:
- Mortgage Payment Calculator
- Loan Principal Calculator
- Monthly Payment Calculator
- Return on Investment Calculator
What is a Mortgage Point?
A **Mortgage Point**, also known as a **Discount Point**, is an upfront fee paid to the lender in exchange for a lower interest rate. One point typically equals 1% of the total loan principal. By paying points, the borrower effectively pre-pays some of the interest, leading to a reduced monthly payment and lower total interest paid over the loan’s lifetime.
The decision to buy points hinges on the **Break-Even Point (BEP)**. The BEP is the amount of time (in months) required for the monthly savings from the lower interest rate to equal the initial cost of the points. If a homeowner plans to keep the mortgage longer than the calculated BEP, buying points is a good financial decision; if they plan to sell or refinance earlier, it is not cost-effective.
Mortgage points are a common tool for borrowers seeking to optimize their long-term housing costs. While the upfront cost is higher, the guaranteed reduction in the monthly rate provides a predictable return on investment. Our calculator simplifies the complex financial calculation of the BEP, helping you make the right choice.
How to Calculate Break-Even Point (Example)
Scenario: Loan $P$ of \$250,000, 30-year term. Original Rate $R_{orig}$=7.0%. New Rate $R_{new}$=6.5%. Points Cost $C_P$= \$2,500.
- Calculate Original Monthly Payment ($M_{orig}$):
At 7.0%, the monthly payment ($M_{orig}$) is calculated to be approximately **\$1,663.26**.
- Calculate New Monthly Payment ($M_{new}$):
At 6.5%, the monthly payment ($M_{new}$) is calculated to be approximately **\$1,580.17**.
- Determine Monthly Savings:
Monthly Savings = $M_{orig} – M_{new} = \$1,663.26 – \$1,580.17 = \$83.09$
- Calculate Break-Even Point (BEP):
$$ BEP = \frac{C_P}{\text{Monthly Savings}} = \frac{\$2,500}{\$83.09} \approx 30.09 \text{ months} $$
- Conclusion:
The Break-Even Point is 30.09 months (or 2.51 years). If the homeowner keeps the loan longer than this period, the points will save them money overall.
Frequently Asked Questions (FAQ)
Generally, discount points paid on a loan used to buy or build your main home can be deducted as prepaid interest in the year they were paid. However, rules are complex; consult a tax advisor for current details.
Q: Can I finance the cost of the points?Yes, many lenders allow you to finance the cost of the points by adding them to the loan principal. However, this increases the loan amount, which means you pay interest on the points themselves.
Q: What is the difference between discount points and origination points?Discount points are paid to reduce the interest rate. Origination points are paid to the lender for processing the loan and do not reduce the rate; they are purely a loan fee.