Annuity Due vs Ordinary Annuity: The Simple Present Value Formula Guide

Key Takeaways

• The timing of payments decides if it's an annuity due or ordinary annuity.
   
• Annuity due gives higher present value since money comes in earlier.
   
• Ordinary annuity pays at the end of every period.
   
• Always use the right formula or calculator so you don't mess up the numbers.

Bonus Tip: A tiny shift to annuity due payments can boost present value by 5-10% or more over long terms due to extra compounding time. 

Sarah, a 58-year-old teacher, put money aside for retirement over many years. She bought an annuity to bring in regular cash once she stopped working. One choice sent money at the start of each month. The other waited until the end. That little change in timing made a difference in how much her savings were worth right now. Knowing annuity due and ordinary annuity makes it easier for people to handle their money plans.

What Is Annuity Due?

An annuity due pays right at the start of each period. Rent works like this. You hand over the money on the first day of the month. Payments arrive early. They lose less to interest as time goes on. That makes the present value higher than the same payments sent at the end, which is what the present value of annuity due formula clearly shows.

What is an ordinary annuity?

An ordinary annuity pays at the end of each period. You see this a lot with loans, bond interest payments, and some retirement checks. Payments come later, so each one gets discounted for one extra period compared to an annuity due. That small delay lowers the present value just a bit.

Key Differences Between Annuity Due and Ordinary Annuity

These points make it clear how timing changes the two annuities a lot.
 

Tiny timing change makes a difference, pick the right one carefully.

Formulas With Examples

Formulas

• Present value of an ordinary annuity PV = PMT × [1 − (1 + r)^−n] / r
• Present value of an annuity due (direct form) PV due = PMT × [1 − (1 + r)^−n] / r × (1 + r)

Note: This is the present value of annuity due formula (also called the annuity due present value formula) for direct calculation. Another way to write it:

PV due = PMT + PMT × [1 − (1 + r)^−(n−1)] / r

Important periodic note

Always change the yearly rate to the rate per period and match the number of periods. For monthly payments at 6% a year, use 0.5% per month and count months for n.

Example using Sarah

Sarah gets ₹20,000 each month for 5 years.
 

Ordinary annuity

1. Discount factor: (1 + r)^−n = 1.005^−60 ≈ 0.741372
2. 1 − 0.741372 = 0.258628
3. Divide by r: 0.258628 / 0.005 ≈ 51.72556
4. PV = 20,000 × 51.72556 ≈ ₹1,034,511

Annuity due

Take the ordinary PV and multiply by (1 + r). PV due = ₹1,034,511 × 1.005 ≈ ₹1,039,684

Sarah gets payments one period sooner with annuity due, so present value goes up by about ₹5,173 over five years. The first payment hits at time zero, meaning one less discount step. That simple shift explains the extra value.

What Is an Ordinary Annuity and Annuity Due Calculator?

An annuity calculator is a free online tool. It finds present value or future value of steady payments fast. You skip doing math by hand, just fill in a few boxes and see the answer.

Most ask for:
 

These come in handy for retirement income, loans, leases, or checking investment growth.

Ordinary Annuity Calculator

This one handles payments at the end of each period. It fits loans, bonds, and many retirement checks.

It uses:

PV = PMT × [1 − (1 + r)^−n] / r

Popular Calculator:

• Present Value of Annuity Calculator by CalculatorSoup
• Annuity Calculator by Bankrate
• Present Value of Annuity Calculator by FinanceFormulas

Annuity Due Calculator

This handles payments at the start of each period. The first payment comes right away, so present value ends up a touch higher than ordinary.

It uses:

PV due = PMT × [1 − (1 + r)^−n] / r × (1 + r)

Popular Calculator:

• Annuity Due Calculator by Omni Calculator
• Present Value of Annuity Due Calculator by CalculatorSoup
• Annuity Due Calculator by FinanceFormulas

Both types work much the same. The big change comes from when payments hit, which shifts the final number.

Uses of Annuity Due and Ordinary Annuity

• Annuity due
  • Rent and lease payments paid up front
  • Some insurance premiums that start coverage right away
     
• Ordinary annuity
  • Loan repayments and many bonds
  • Most pension and retirement payouts that arrive at period end

Conclusion

Timing really counts. Shift a payment from end to start, and you get cash sooner, that bumps up present value. Stick to the ordinary annuity formula for end-of-period stuff. Switch to the annuity due formula or just multiply by (1 + r) for start-of-period ones. That small gap can shake up your long-term plans. Always check your contract type and plug the numbers into a calculator first. It might save you a nice chunk down the road.

FAQs

What is the formula for annuity due?

PV due = PMT × [1 − (1 + r)^−n] / r × (1 + r)

How do you convert ordinary annuity to annuity due?

Multiply the ordinary annuity PV by (1 + r).

Annuity a bad investment if you collect immediately?

No, collecting right away (annuity due) often gives higher present value.

How does payment timing affect the present value of an annuity?

Earlier payments (annuity due) increase present value; later ones (ordinary annuity) decrease it.

How to decide if an annuity is good or bad?

Check returns, fees, inflation impact, payout timing, and flexibility. If it gives stable income with low cost, it is good.