Saving
Time to reach a savings goal
The compound growth formula solved for the number of periods. Use the monthly rate and a monthly deposit so n comes out in months.
The Formula
n = ln((FV x r + PMT) / (PV x r + PMT)) / ln(1 + r)
The compound growth formula solved for the number of periods. Use the monthly rate and a monthly deposit so n comes out in months.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| FV | Target balance | currency | The future dollar amount you want the account to hold. Inflate it to future prices if it is tied to something you will buy later. |
| PV | Balance already saved | currency | Today's starting amount. Zero is fine; the formula handles it as long as PMT is positive. |
| PMT | Deposit each period | currency | Assumed constant and deposited at the end of each period. Varying contributions need a month-by-month simulation instead. |
| r | Periodic interest rate | decimal | Annual percentage yield divided by the number of deposits per year. A 5% APY with monthly deposits gives r = 0.05/12 = 0.00416667. |
| n | Number of periods until the goal | periods | Divide by 12 for years when using monthly inputs. Round up — you reach the target partway through a real month. |
What Each Symbol Means
FVcurrency
Target balance
The future dollar amount you want the account to hold. Inflate it to future prices if it is tied to something you will buy later.
PVcurrency
Balance already saved
Today's starting amount. Zero is fine; the formula handles it as long as PMT is positive.
PMTcurrency
Deposit each period
Assumed constant and deposited at the end of each period. Varying contributions need a month-by-month simulation instead.
rdecimal
Periodic interest rate
Annual percentage yield divided by the number of deposits per year. A 5% APY with monthly deposits gives r = 0.05/12 = 0.00416667.
nperiods
Number of periods until the goal
Divide by 12 for years when using monthly inputs. Round up — you reach the target partway through a real month.
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.