Time to Reach FV Goal
How long to accumulate a target amount through regular annual payments.
When to use: Use to find how long a savings plan takes to reach a financial goal.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| n | Number of Years | Time to reach target | years |
| FV | Future Value | Savings goal | $ |
| PMT | Payment | Annual savings amount | $ |
| k | Interest Rate | Annual return | % |
Real-Life Examples
Example 1: Retirement Timeline
Save $10,000/year at 8%. How long to reach $500,000?
Given
Step-by-Step
It takes about 20.91 years to save $500,000.
Example 2: Down Payment Goal
Save $5,000/year at 4% to reach $40,000.
Given
Step-by-Step
About 7 years to save $40,000 for a down payment.
Frequently Asked Questions
Enter the goal amount as FV, your annual savings as PMT, and expected return as k. The formula accounts for both your contributions and the compound growth of all previously deposited money.
This formula assumes you start from zero. If you have an existing balance, you need a combined formula that accounts for both the lump-sum growth of your current balance and the annuity growth of future contributions.
Higher contributions shorten the time to reach your goal significantly. Doubling your contribution more than halves the time because the larger deposits also earn more interest, creating a compounding advantage on top of the larger base.