Determine how much time and interest you can save by making extra principal payments on your mortgage.
Mortgage Payoff Calculator
Mortgage Payoff Formula
The calculation involves two main steps: calculating the original minimum monthly payment and then calculating the new number of payments needed with the extra amount.
1. Calculate the Required Monthly Payment ($M$):
$$M = P \frac{r(1+r)^n}{(1+r)^n - 1}$$
2. Calculate the New Number of Months ($n’$):
$$n' = \frac{\ln\left(\frac{M_{actual}}{M_{actual} - P \cdot r}\right)}{\ln(1+r)}$$
Where: $P$ = Principal Loan Amount, $r$ = Monthly Rate, $n$ = Original Months, $M_{actual}$ = $M + E$ (Extra Payment).
Formula Source: Investopedia (Amortization Formula), The Balance (Loan Payoff)
Variables
- Loan Amount ($): The initial amount borrowed.
- Annual Interest Rate (%): The yearly interest rate (APR) applied to the loan.
- Original Loan Term (Years): The planned repayment period, typically 15 or 30 years.
- Extra Monthly Principal Payment ($): The additional amount you commit to paying each month directly against the principal.
Related Calculators
- Mortgage Payment Calculator
- Bi-Weekly Payment Calculator
- Refinance Break-Even Calculator
- Interest Savings Calculator
What is Mortgage Payoff?
Mortgage payoff refers to the final act of paying off the entire remaining principal balance of your home loan. For most homeowners, the primary goal is to accelerate this process to save substantial money on interest and gain full equity in the property sooner.
Accelerating the payoff, often through extra principal payments, significantly reduces the loan term. Since interest is calculated daily on the outstanding principal, reducing the principal balance faster means less interest accrues over the life of the loan. This calculator models the most common payoff acceleration method: making consistent, extra monthly payments.
How to Calculate Mortgage Payoff (Example)
- Gather Inputs: Assume a $250,000 loan, 30-year term, 5.5% rate, and a $100 extra monthly payment.
- Determine Monthly Rate ($r$): Divide the annual rate by 12 and 100: $5.5 / 12 / 100 \approx 0.004583$.
- Calculate Original Payment ($M$): Use the amortization formula to find the standard payment, which is approximately $1,419.47$.
- Determine Actual Payment ($M_{actual}$): Add the extra payment: $1,419.47 + $100.00 = $1,519.47$.
- Calculate New Term ($n’$): Use the new term formula with $M_{actual}$. The result is a new term of approximately 324 months.
- Convert to Time Saved: The original term was 360 months (30 years). The new term is 324 months (27 years). Time saved is 3 years!
Frequently Asked Questions (FAQ)
Is it better to pay extra principal or invest the money?
This depends on the mortgage interest rate versus your expected investment return. If your mortgage rate is high (e.g., 7% or more), paying off the mortgage is often the safer, guaranteed return. If your rate is low (e.g., 4% or less), investing may yield a higher return.
What is the fastest way to pay off a mortgage?
The fastest ways are either making lump-sum payments (e.g., from a bonus) or committing to a bi-weekly payment schedule (which is equivalent to making one extra monthly payment per year).
Can I use this calculator for other types of loans?
Yes, the underlying amortization formula works for any fixed-rate installment loan, such as car loans or personal loans, provided the interest is compounded monthly.
Does the extra payment go directly to the principal?
Yes, but you must clearly specify to your lender that the excess amount is to be applied directly to the principal balance, not held for the next month’s payment.