FV of Annuity Due
Future value of an annuity due (discrete annual beginning-of-period payments) compounded continuously.
When to use: Use when payments arrive at the start of each year but the rate is continuously compounded — the standard convention in continuous-time finance.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| FVA | Future Value of Annuity Due | Total future value of beginning-of-period payments | $ |
| PMT | Payment | Periodic payment amount (paid at start of period) | $ |
| k | Interest Rate | Nominal annual interest rate | % |
| n | Number of Years | Time period in years | years |
Real-Life Examples
Example 1: Continuous Due Accumulation
$5,000/year deposited at start of year, 6% continuous compounding for 20 years.
Given
Step-by-Step
Beginning-of-year deposits grow to $199,201.37 with continuous compounding.
Example 2: Academic Example
$2,000/year at start, 8% continuous compounding for 10 years.
Given
Step-by-Step
The annuity due grows to $31,880.40 with discrete annual deposits and continuous compounding.
Frequently Asked Questions
It multiplies the continuous ordinary annuity FV by e^k, which accounts for each payment being made one period earlier and thus earning one extra period of continuous interest growth.
For annual compounding, the due factor is (1+k). For continuous compounding, it is e^k, which is always slightly larger. At k=6%, (1+k)=1.06 while e^k=1.0618.
Primarily in academic finance courses and theoretical research. In practice, the m-times annuity due formula with high m provides nearly identical results.