Retirement
Level payment from a lump sum
The present value of an annuity solved for the payment. Every symbol is either something you set or something you already have.
The Formula
PMT = PV x r x (1 + r)^n / ((1 + r)^n - 1)
The present value of an annuity solved for the payment. Every symbol is either something you set or something you already have.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| PV | Starting balance | currency | Where it is drawn from matters for tax, not for this arithmetic. |
| r | Periodic return | decimal | Annual expected return divided by payments per year. A 5% annual return with monthly payments gives 0.00416667. |
| n | Total number of payments | periods | Years multiplied by payments per year — 25 years monthly is 300. |
| PMT | Payment per period | currency | The account reaches exactly zero after n payments at this amount, assuming every assumption holds. |
What Each Symbol Means
PVcurrency
Starting balance
Where it is drawn from matters for tax, not for this arithmetic.
rdecimal
Periodic return
Annual expected return divided by payments per year. A 5% annual return with monthly payments gives 0.00416667.
nperiods
Total number of payments
Years multiplied by payments per year — 25 years monthly is 300.
PMTcurrency
Payment per period
The account reaches exactly zero after n payments at this amount, assuming every assumption holds.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate annuity payments 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 Annuity Payments, filed under Finance. Every number the guide produces comes from substituting into this one line.