Payment from FV
Beginning-of-period payment to reach a future value with periodic compounding.
When to use: Use for monthly savings goals with beginning-of-month deposits.
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 |
| m | Compounding Frequency | Compounding periods per year | integer |
Real-Life Examples
Example 1: Monthly Savings
Save for $50,000 in 5 years at 5% monthly compounding, deposit at start of month.
Given
Step-by-Step
Deposit $731.78 at the start of each month to reach $50,000.
Example 2: Quarterly Fund
Accumulate $75,000 in 8 years, 6% quarterly compounding, deposit at start of quarter.
Given
Step-by-Step
Deposit $1,816.04 at the start of each quarter.
Frequently Asked Questions
Enter the target amount as FV, annual rate as k, years as n, and 12 for m. The result is the monthly beginning-of-month deposit needed to reach your goal, accounting for the extra interest earned from early-month timing.
Beginning-of-month deposits earn interest for the full month, while end-of-month deposits earn nothing until the next period. Over many years, this timing difference reduces the total deposits needed to reach the same goal.
Yes, if your payroll deposits hit your investment account at the start of each pay period. For biweekly pay, set m=26. For monthly pay deposited at the start of the month, set m=12.