Formula & Calculator
Annuity Due Future Value
Calculates the future value of a series of equal payments made at the beginning (rather than end) of each period.
Interpretation
FV (due) = PMT × (((1+r)^n − 1)/r) × (1+r). Future value of an annuity with payments at the beginning of each period. Used in savings and retirement planning.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| FV (due) | Future value of annuity due | currency |
| PMT | Regular payment amount | currency |
| r | Interest rate per period | |
| n | Number of periods |
What it means
The annuity due future value formula calculates the accumulated value of a series of equal payments made at the beginning of each period, instead of at the end (ordinary annuity). Because each payment earns interest for one extra period, the future value is the ordinary annuity value multiplied by (1+r). It is used for rental payments, insurance premiums, and savings plans where contributions are made at the start of each period. Understanding this formula helps in planning for retirement and in comparing different savings strategies.
Worked example
Annuity Due Future Value – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| PMT | 200 |
| r | 0.005 |
| n | 120 |
| Parameter | Value |
|---|---|
| PMT | 500 |
| r | 0.005833 |
| n | 240 |
Common mistakes
- Annuity due future value: Future value of an annuity where payments occur at the beginning of each period.
- PMT: The periodic payment amount – same for each period.
- r: Interest rate per period – in decimal.
- n: Number of payments.
- The (1+r) factor: Accounts for the fact that each payment earns one extra period of interest compared to an ordinary annuity.
- Compare: FV(due) = FV(ordinary) × (1+r).
Applications
The future value of an annuity due accounts for payments made at the beginning of each period, adding one extra period of compounding compared to an ordinary annuity. This is relevant for lease payments, insurance premiums, and retirement contributions made at the start of the period. By using the annuity due formula, professionals can accurately value investments that require up‑front payments. This is also used in financial planning to compare the outcomes of different payment timings. Understanding annuity due helps in making decisions about savings, annuities, and loan structures. It is a key concept in time value of money applications.
- Valuation of lease agreements with advance payments
- Retirement savings contributions at the start of the period
- Insurance premium calculation and policy valuation
- Comparison of investment options with different payment timing
- Financial planning and annuity product analysis
Frequently Asked Questions
FV (due) = PMT × (((1+r)^n − 1) / r) × (1+r). An annuity due has payments at the beginning of each period, so each payment earns one extra period of interest compared to an ordinary annuity (payments at end).
It is used when payments are made at the start of the period, such as rent payments, insurance premiums, or some savings plans where contributions are made at the beginning.
The future value of an annuity due is larger by a factor of (1+r) compared to the ordinary annuity. This can be significant for long‑term investments.
FV_due = FV_ordinary × (1+r). PV_due = PV_ordinary × (1+r). This holds for both present and future values.
If payments vary, you cannot use the simple formula. You would need to compound each payment separately to the future date.
- Using the ordinary annuity formula for payments at the beginning.
- Forgetting to multiply by (1+r) when converting from ordinary to due.
- Not adjusting the number of periods when switching.
If contributions are made at the beginning of each month, they earn interest for that month. The annuity due formula correctly accounts for this, yielding a higher future value.
r = 0.06/12 = 0.005, n = 5×12 = 60. FV_ordinary = 100 × ((1.005^60 − 1)/0.005) ≈ 100 × 69.77 = 6,977. FV_due = 6,977 × 1.005 ≈ 7,012.
More frequent compounding increases the effective rate, raising the future value. The formula already uses the periodic rate that matches the payment frequency.
An annuity due is a stream of multiple payments. A lump sum is a single payment. The annuity due future value is the sum of compounded payments, each with its own growth period.