Saving
Deposit needed to hit a deadline
The inverse question: given a fixed number of months, what monthly deposit closes the gap. This is the form to use when the deadline is not negotiable.
The Formula
PMT = (FV - PV x (1 + r)^n) x r / ((1 + r)^n - 1)
The inverse question: given a fixed number of months, what monthly deposit closes the gap. This is the form to use when the deadline is not negotiable.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| n | Number of periods allowed | periods | Months remaining until the deadline, multiplied by the deposits per year. |
| PMT | Required deposit per period | currency | Lower than the naive gap-over-time figure, because the balance earns interest along the way. |
What Each Symbol Means
nperiods
Number of periods allowed
Months remaining until the deadline, multiplied by the deposits per year.
PMTcurrency
Required deposit per period
Lower than the naive gap-over-time figure, because the balance earns interest along the way.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate how long it takes to reach a savings goal 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 How Long It Takes To Reach A Savings Goal, filed under Finance. Every number the guide produces comes from substituting into this one line.