Annuity Due

What is an annuity due?

An annuity due is a series of equal payments made at the beginning of each period. Common examples include rent and many insurance premiums, which are typically payable at the start of each coverage period.

How it works

Because payments occur at the start of each period, each payment of an annuity due is invested or available to the recipient one period earlier than an ordinary annuity (where payments occur at the end of the period). This timing affects the present and future values of the cash flows and the opportunity to earn interest.

Income from annuities is generally taxed as ordinary income.

Annuity due vs. ordinary annuity

• Annuity due: payments at the beginning of each period (beneficial to the recipient).
• Ordinary annuity: payments at the end of each period (often preferred by the payer).

The one-period earlier timing of annuity due payments increases both present and future values compared with otherwise identical ordinary annuities.

Examples

• Annuity due: rent paid at the start of the month, insurance premiums due at the start of a coverage period.
• Ordinary annuity: mortgage or loan payments often scheduled at the end of each payment period.

Calculations

Let:
– C = cash flow per period
– i = interest rate per period
– n = number of payments

Present value (PV) of an annuity due:
PV_due = C * [1 − (1 + i)^−n] / i * (1 + i)

Future value (FV) of an annuity due:
FV_due = C * [ (1 + i)^n − 1 ] / i * (1 + i)

(These are the ordinary-annuity formulas multiplied by (1 + i) to reflect payments occurring one period earlier.)

Example:
Receive $1,000 at the beginning of each year for 10 years at 3% annual interest.
– PV_due = 1,000 * [1 − (1.03)^−10] / 0.03 * 1.03 ≈ $8,786.14
– FV_due = 1,000 * [(1.03)^10 − 1] / 0.03 * 1.03 ≈ $11,807.80

Immediate annuity and whole-life annuity

• Immediate annuity: funded with a lump sum and begins paying out immediately; payments can be for a fixed term or lifetime.
• Whole-life annuity: pays the annuitant for life, usually with payments at the beginning of each period if structured as an annuity due.

What happens when an annuity expires?

When an annuity’s term ends (or upon the annuitant’s death if not a life-contingent product), the contract terminates and no further payments are made unless a contract provision or beneficiary designation specifies otherwise.

Which is better: annuity due or ordinary annuity?

It depends on perspective:
– Recipient prefers annuity due because earlier payments increase present value and allow immediate use or investment.
– Payer prefers ordinary annuity because they retain funds longer before paying.

Choice is typically contract-driven rather than optional for the parties.

Summary

An annuity due requires payments at the beginning of each period, increasing the value of payments relative to an ordinary annuity. Use the (ordinary annuity formula) × (1 + i) to convert present- and future-value calculations for annuity due scenarios. Examples include rent and many insurance premiums; mortgages and many loans are ordinary annuities.