Time from Lump Sum
Time for a lump sum to grow to a target with periodic compounding.
When to use: Use with monthly or quarterly compounding to find time to reach a goal.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| n | Number of Years | Time to reach goal | years |
| FV | Future Value | Target value | $ |
| PV | Present Value | Starting amount | $ |
| k | Interest Rate | Nominal annual rate | % |
| m | Periods/Year | Compounding frequency | integer |
Real-Life Examples
Example 1: Monthly CD Doubling
How long to double $10,000 at 5% compounded monthly?
Given
Step-by-Step
With monthly compounding at 5%, doubling takes about 13.89 years.
Example 2: Quarterly Growth
How long for $30,000 to reach $50,000 at 6% quarterly?
Given
Step-by-Step
It takes about 8.58 years with quarterly compounding.
Frequently Asked Questions
Yes, but only slightly. Monthly compounding reaches a goal a bit faster than annual compounding at the same nominal rate. The improvement is more noticeable at higher interest rates and for longer time periods.
Use this formula with FV = 2 × PV, your annual rate as k, and m = 12. The result is the number of years to double with monthly compounding, which will be slightly less than with annual compounding.
The formula converts the periodic growth factor into an annual equivalent. The term m × ln(1 + k/m) represents the effective annual growth rate in logarithmic terms, accounting for the compounding frequency.