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FIRE calculator: years to a savings target

Estimate the years until a savings target is reached from a current balance, yearly contributions and a real annual return.

By Fintrivex Updated Sources

Inputs

Goal

In today’s dollars.

Only sizes the yearly income a balance equals.

Savings

Added at the end of each year.

After inflation.

Estimated time to target

13.79 years

About 13 years, 9 months to reach $1,500,000

Breakdown

Target balance
$1,500,000.00
Current balance
$285,000.00
Annual contribution (year end)
$42,000.00
Real annual return
6.00%
Years to target
13.79
Income at 4.00% of target
$60,000.00

What changes

  • Reaching $1,500,000 from $285,000 takes 13.79 years at 6.00% real return with $42,000 added each year.
  • At a 4.00% withdrawal rate, the target equals $60,000 a year and the current balance equals $11,400 a year.
Balance over time

Scrub across years to read values

Year 14: $1,526,990.40

  • Balance

Year-by-year balance

YearContributionGrowthBalance
1$42,000$17,100$344,100
2$42,000$20,646$406,746
3$42,000$24,405$473,151
4$42,000$28,389$543,540
5$42,000$32,612$618,152
6$42,000$37,089$697,241
7$42,000$41,834$781,076
8$42,000$46,865$869,940
9$42,000$52,196$964,137
10$42,000$57,848$1,063,985
11$42,000$63,839$1,169,824
12$42,000$70,189$1,282,014
13$42,000$76,921$1,400,934
14$42,000$84,056$1,526,990
  • The return is real, meaning after inflation, so the target is in today's dollars. It is an assumption you enter, not a forecast.
  • Contributions are added at the end of each year. The years figure comes from n = ln((T*r + C) / (S*r + C)) / ln(1 + r) and can include a fraction of a year; the table shows whole years.
  • Taxes, fees and changes in spending are not modeled. The withdrawal rate only sizes the income a balance equals.

Estimated time to target

13.79 years

See breakdown

What to check next

How it works

What this calculation includes

The balance after k years is S(1 + r)^k plus C((1 + r)^k - 1) / r. Setting that equal to the target T and solving for k gives the formula above.

With a target of $1,500,000, a current balance of $285,000, $42,000 added each year and a 6% real return, the result is 13.79 years.

At a zero return the balance grows only by contributions, so the time is the shortfall divided by the yearly contribution. If the current balance is already at or above the target, the time is zero.

Years to a savings target

n = ln ⁡ ( T ⁢ r + C S ⁢ r + C ) ln ⁡ ( 1 + r )

In words Solve for the time when today’s balance, grown at a real return with a yearly contribution, reaches the target.

n
Years to the target
T
Target balance
S
Current savings
C
Contribution added at the end of each year
r
Real (after-inflation) annual return

If r = 0, n = (T − S) ÷ C.

Example

  • Target T: $1,500,000.00
  • Saved S: $285,000.00
  • Yearly contribution C: $42,000.00
  • Real return r: 6%
  1. n = ln((T·r + C) ÷ (S·r + C)) ÷ ln(1 + r)
  2. Computed years = 13.79

Years to target: 13.79 years

Worked example

Using the default inputs on this page.

Target balance
$1,500,000.00
Withdrawal rate
4.00%
Current balance
$285,000.00
Contribution per year
$42,000.00
Real annual return
6.00%

Estimated time to target

13.79 years

About 13 years, 9 months to reach $1,500,000

Questions

What does a real return mean?

A return after inflation. Using a real return keeps the target and contributions in today's dollars.

When are contributions added?

At the end of each year, after that year's growth.

Why is the answer not a whole number?

The formula solves for the time at which the balance equals the target, which can fall part way through a year. The table shows whole years.

What does the withdrawal rate do?

It only sizes the yearly income a balance equals, as the balance times the rate. It does not change the years to target.

Sources

Methodology and worked examples