Payment from FV
Beginning-of-period payment needed to reach a future value goal.
When to use: Use to find how much to save at the start of each year to reach a goal.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PMT | Payment | Periodic payment amount (paid at start of period) | $ |
| FV | Future Value | Future lump sum value | $ |
| k | Interest Rate | Nominal annual interest rate | % |
| n | Number of Years | Time period in years | years |
Real-Life Examples
Example 1: College Savings
Need $200,000 for college in 18 years, 7% return, deposits at start of year.
Given
Step-by-Step
Save $5,497.31 at the start of each year for college.
Example 2: Business Expansion Fund
Accumulate $500,000 in 10 years at 6%, deposits at start of year.
Given
Step-by-Step
Deposit $35,793.30 at the start of each year for the expansion fund.
Frequently Asked Questions
Enter your target amount as FV, expected return as k, and years as n. The formula gives the beginning-of-year deposit needed. Because deposits earn interest from day one of each year, the required amount is slightly less than end-of-year deposits.
Depositing at the start of each year gives your money a full year of interest before the next deposit. Over long time horizons, this timing advantage compounds significantly, requiring smaller total deposits to reach the same goal.
If you make annual contributions to a 529 plan at the start of each year (like January), use this formula. It tells you the annual deposit needed to reach your college savings target, accounting for the early-year timing of each contribution.