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.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| n | Number of Years | Time to reach the goal | years |
| FV | Future Value | Target future value | $ |
| PV | Present Value | Starting amount | $ |
| k | Interest Rate | Annual rate | % |
Real-Life Examples
Example 1: Doubling Time
How long to double $50,000 at 7% annually?
Given
Step-by-Step
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
Step-by-Step
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.