David is a Chartered Financial Analyst and a 15-year veteran of the mortgage industry, specializing in refinance analysis and interest rate optimization.
This 4-in-1 Refinance calculator helps you model your new loan. Enter any three values for your new refinanced loan—Principal, Rate, Term, or Payment—and we will solve for the fourth.
Refinance Calculator
Refinance (Amortization) Formulas
i = R / 12 / 100 (Monthly Rate)
n = T * 12 (Number of Months)
Solve for Monthly Payment (M):
M = P * [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Solve for Loan Amount (P):
P = M * [ (1 + i)^n – 1 ] / [ i(1 + i)^n ]
Solve for Term (n):
n = log( M / (M – P*i) ) / log(1 + i)
Solve for Rate (i):
(No direct formula; solved iteratively)
Formula Variables
- (P) New Loan Amount: The total principal balance of your new refinance loan.
- (R) New Annual Rate: The new Annual Percentage Rate (APR) you will receive.
- (T) New Loan Term: The new term for the loan (e.g., 15 or 30 years).
- (M) New Monthly Payment: The new fixed monthly payment (Principal & Interest).
Related Calculators
- Mortgage Payment Calculator
- Loan Payoff Calculator
- Loan to Value (LTV) Calculator
- Debt to Income (DTI) Calculator
What is a Refinance?
A refinance is the process of replacing your existing loan (most commonly a mortgage) with a new one. Your new loan pays off the old loan’s balance, and you begin making payments on the new loan, which will have a new loan amount (P), new interest rate (R), and new term (T).
People refinance for several main reasons:
1. To get a lower interest rate (R): This is the most popular reason. A lower rate reduces your monthly payment (M) and saves you significant money on total interest.
2. To change the term (T): You might refinance from a 30-year loan to a 15-year loan to pay off your home much faster.
3. To cash out equity: A “cash-out refinance” involves taking a new loan (P) that is larger than your old balance, and you receive the difference in cash.
This calculator helps you model the new loan’s parameters. You can compare the new (M) Monthly Payment it calculates to your current payment to see your monthly savings. You can also solve for (R) to see what rate you would need to achieve a desired payment.
How to Calculate a Refinance (Example)
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Identify New Loan Variables
You are refinancing your remaining mortgage balance to a new 30-year loan:
• New Loan Amount (P): $300,000
• New Annual Rate (R): 5.99%
• New Loan Term (T): 30 years -
Convert to Monthly Terms (i, n)
The formula uses monthly values:
• Monthly Rate (i): 5.99% / 12 / 100 = 0.0049917
• Number of Months (n): 30 years * 12 = 360 -
Choose the Payment Formula
Use the standard formula to solve for Monthly Payment (M):
M = P * [ i(1 + i)^n ] / [ (1 + i)^n – 1 ] -
Calculate the Monthly Payment
Plug in the monthly values:
• Numerator: 0.0049917 * (1 + 0.0049917)^360 = 0.02996
• Denominator: (1 + 0.0049917)^360 – 1 = 5.002
M = $300,000 * [ 0.02996 / 5.002 ]
M = $300,000 * 0.005989 = $1,796.70
Your new monthly payment will be $1,796.70.
Frequently Asked Questions (FAQ)
When should I refinance?
The old “1% rule” (refinance if rates are 1% lower) is outdated. Today, even a 0.5% rate drop can save you money. The real question is how long it takes for your monthly savings to cover your closing costs (the “break-even point”). If you plan to stay in the home longer than your break-even point, refinancing is often a good idea.
What is a “cash-out” refinance?
This is when your new loan amount (P) is *larger* than your old loan’s balance. You “cash out” the difference. For example, if you owe $250,000 and refinance for $300,000, you get $50,000 in cash. This is a common way to pay for home improvements.
What is a “rate and term” refinance?
This is the most common type, where you are only changing the interest rate (R) and/or the term (T) of your loan. Your new loan amount (P) is just the balance of your old loan plus any closing costs you roll in.
Will refinancing restart my loan term?
Yes, usually. If you are 5 years into a 30-year loan and refinance into a *new* 30-year loan, your payoff date is extended. However, many people refinance into a shorter term (like 20 or 15 years) to pay the loan off faster.