Present Value of an Annuity Due
An annuity due is an annuity where each payment comes at the start of the period instead of the end, like rent or lease payments. Because every payment arrives one period earlier, its present value is the ordinary annuity value multiplied by (1 + r).
Annuity due explained simply
An annuity due pays at the start of each period, so every payment arrives one period earlier than in an ordinary annuity. Value it as an ordinary annuity and multiply by (1 + r). In the example, $1,000 a year for 5 years at 6%, starting today, is worth about $4,465.11.
What this annuity due lesson covers
- What an annuity due (annuity in advance) is
- How it differs from an ordinary annuity
- The annuity due formula: ordinary annuity × (1 + r)
- Spotting annuity due wording in exam questions
Annuity due formula, explained
- C
- equal payment at the start of each period
- r
- discount rate per period
- n
- number of payments
- C
- first payment, received today
- n − 1
- remaining payments, treated as an ordinary annuity
How to value an annuity due step by step (worked example)
You receive $1,000 at the start of each year for 5 years, with the first payment today. The discount rate is 6%. What is it worth today?
- Value it as an ordinary annuity first: $1,000 × [1 − (1.06)⁻⁵] ÷ 0.06 ≈ $4,212.36.
- Shift every payment one year earlier: multiply by 1.06.
- PV_due ≈ $4,212.36 × 1.06 ≈ $4,465.11.
Answer: About $4,465.11 today (rounded to the cent), versus $4,212.36 for the ordinary annuity.
Annuity due vs ordinary annuity
| Annuity due | Ordinary annuity | |
|---|---|---|
| First payment | Today | End of the first period |
| Formula | Ordinary annuity × (1 + r) | C × [1 − (1 + r)⁻ⁿ] ÷ r |
| Value here | $4,465.11 | $4,212.36 |
| Calculator mode | BEGIN | END |
Harder annuity due questions
A $10,000 lease is paid in 5 yearly payments at the start of each year, at 6%. What's the payment?
Divide by the annuity-due factor: 10,000 ÷ (4.212364 × 1.06) ≈ $2,239.59, lower than the $2,373.96 for end-of-year payments, because the lender gets the money sooner.
Why is the annuity due worth exactly 6% more?
Every payment moves one year closer to today, so each is discounted one year less. That multiplies the whole value by 1.06.
Common annuity due questions
What is the formula for the present value of an annuity due?
PV = C × [1 − (1 + r)⁻ⁿ] ÷ r × (1 + r). It is the ordinary annuity formula multiplied by (1 + r), because every payment arrives one period earlier and is discounted one period less.
What is the difference between an annuity due and an ordinary annuity?
In an ordinary annuity payments come at the end of each period, like most loan payments. In an annuity due they come at the beginning, like rent. The annuity due is always worth more today at a positive rate.
How do I calculate an annuity due on a financial calculator?
Switch the calculator to beginning mode, usually shown as BGN, then enter N, I/Y and PMT and compute PV as usual. Remember to switch back to END mode afterwards.
What is an advanced annuity?
Advanced annuity, or annuity in advance, is another name for an annuity due: a series of equal payments made at the start of each period. The same formula applies.