Loans & Debt
Loan payment
The annuity formula gives the payment for a given balance, rate and term.
The Formula
Pmt = balance x r x (1+r)^n / ((1+r)^n - 1)
The annuity formula gives the payment for a given balance, rate and term.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| B | Balance | currency | Outstanding principal. |
| r | Monthly rate | rate | Annual rate divided by twelve. |
| n | Months | count | Number of payments remaining. |
What Each Symbol Means
Bcurrency
Balance
Outstanding principal.
rrate
Monthly rate
Annual rate divided by twelve.
ncount
Months
Number of payments remaining.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate refinance savings page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Refinance Savings, filed under Finance. Every number the guide produces comes from substituting into this one line.