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Time from Lump Sum

Find how many years it takes for a present value to grow to a future value.

When to use: Use to determine how long until an investment doubles, triples, or reaches a specific goal.

Calculator

Formula

n=ln(FV/PV)ln(1+k)n = \frac{\ln(FV/PV)}{\ln(1 + k)}

Variables

SymbolNameDescriptionUnit
nNumber of YearsTime to reach the goalyears
FVFuture ValueTarget future value$
PVPresent ValueStarting amount$
kInterest RateAnnual rate%

Real-Life Examples

Example 1: Doubling Time

How long to double $50,000 at 7% annually?

Given

FV = 100,000PV = 50,000k = 0.07

Step-by-Step

1.n = ln(100000/50000) / ln(1.07)
2.n = ln(2) / ln(1.07)
3.n = 0.6931 / 0.0677
4.n = 10.24 years
Result:10.24

It takes about 10.24 years to double your money at 7%.

Example 2: Investment Goal

How long for $25,000 to grow to $80,000 at 9%?

Given

FV = 80,000PV = 25,000k = 0.09

Step-by-Step

1.n = ln(80000/25000) / ln(1.09)
2.n = ln(3.2) / ln(1.09)
3.n = 1.1632 / 0.08618
4.n = 13.50 years
Result:13.50

It takes about 13.5 years to reach $80,000.

Frequently Asked Questions

Divide the natural log of 2 by the natural log of (1 + rate), or use the Rule of 72 as a quick estimate: 72 ÷ rate (as a whole number). At 7%, doubling takes about 10.2 years (exact) or roughly 10.3 years (Rule of 72).

The Rule of 72 is a shortcut to estimate doubling time. Divide 72 by the annual interest rate (as a percentage) to get approximate years to double. For example, at 6% it takes about 72/6 = 12 years. It is most accurate for rates between 4% and 12%.

Yes. Enter any future value target and current amount. The formula works for any growth multiple — tripling, quadrupling, or reaching a specific dollar amount from any starting point.