The Biweekly Mortgage Calculator with Extra Payments is an innovative tool designed to help homeowners explore the potential savings and accelerated payoff schedule from making extra payments on a biweekly basis, rather than the standard monthly payment. This calculator provides users with detailed insights on how much quicker they can pay off their mortgage and how much they can save in interest over the life of the loan by adjusting the frequency and amount of their payments.
Formula
Biweekly Interest Rate Calculation
The biweekly interest rate is calculated by dividing the annual interest rate by 2600, reflecting the 26 biweekly periods in a year:
i = r / (26 * 100)
- i: Biweekly interest rate
- r: Annual interest rate in percent
Total Number of Biweekly Payments
The total number of biweekly payments over the mortgage term is:
n = 26 * T
- n: Total number of biweekly payments
- T: Mortgage term in years
Regular Biweekly Payment
The regular biweekly payment is derive using the formula for an ordinary annuity:
M = P * (i * (1 + i)^n) / ((1 + i)^n - 1)
- M: Regular biweekly payment
- P: Initial principal or loan amount
- i: Biweekly interest rate
- n: Total number of biweekly payments
Biweekly Payment with Extra Payments
When extra payments are add, the total biweekly payment becomes:
M_total = M + E
- M_total: Total biweekly payment including extra payments
- E: Extra payment made each biweekly period
Adjusted Number of Payments with Extra Payments
The new total number of payments with extra payments is recalculate using a logarithmic function:
n_new = log((E + 1) / (E + 1 - P * i)) / log(1 + i)
- n_new: Recalculated number of biweekly payments
Total Payments and Interest
Total payments and the interest paid are calculate for scenarios with and without extra payments:
- Total Payments = M * n
- Total Payments_new = M_total * n_new
- Total Interest = Total Payments_new - P
Savings and Payoff Date
Savings from making extra payments and the estimate payoff date are calculated as:
- Savings = (Total Payments) - (Total Payments_new)
- Payoff Years = n_new / 26
Table for General Terms and Calculations
This table simplifies commonly searched terms related to mortgage payments:
Term | Definition |
---|---|
Biweekly Payment | Payment made every two weeks instead of monthly. |
Extra Payment | Additional amount paid to reduce the principal faster. |
Total Payments | Total amount paid over the life of the mortgage. |
Total Interest | Total interest paid over the life of the mortgage. |
Payoff Date | Estimated date the mortgage will be fully paid off. |
Example
Let's consider a homeowner who has a mortgage with the following details:
- Principal Loan Amount: $300,000
- Annual Interest Rate: 4%
- Loan Term: 30 years
Calculating the Biweekly Interest Rate
First, we calculate the biweekly interest rate by dividing the annual interest rate by 2600 (26 biweekly periods multiplied by 100 to adjust for percentage):
- Biweekly Interest Rate = 4 / 2600 = 0.001538 per biweekly period
Total Number of Biweekly Payments
Next, determine how many biweekly payments the homeowner will make over the life of the loan:
- Total Biweekly Payments = 26 * 30 = 780 payments
Regular Biweekly Payment
Using the formula for calculating the regular biweekly payment:
- Regular Biweekly Payment = 300,000 * (0.001538 * (1 + 0.001538)^780) / ((1 + 0.001538)^780 - 1)
- Regular Biweekly Payment ≈ $770
Biweekly Payment with Extra Payments
If the homeowner decides to make an extra payment of $100 biweekly:
- Total Biweekly Payment with Extra = $770 + $100 = $870
This example illustrates how the Biweekly Mortgage Calculator can be used to determine regular and extra payment amounts, helping homeowners understand their payment options and potentially shorten the term of their mortgage while saving on interest costs.
Most Common FAQs
Savings can be significant, depending on the extra amount paid and the original loan terms.
While making extra payments reduces interest and loan term, it's essential to consider financial stability and other investment opportunities.
The calculator assumes a fixed interest rate for simplicity, though variable rates would require different calculations.