Future Value of an Annuity

The future value (FV) of an annuity is the total value at a future date of a series of equal payments made at regular intervals, assuming a specific interest (or discount) rate. Calculating FV helps assess how recurring payments grow over time due to compound interest.

Key concepts

• Annuity: a series of equal payments made over a set number of periods.
• Ordinary annuity: payments made at the end of each period.
• Annuity due: payments made at the beginning of each period (each payment earns interest for one additional period compared with an ordinary annuity).
• Time value of money: money available today can be invested to earn interest, so its future value is greater.

Formulae

• Future value of an ordinary annuity:
  P = PMT × (((1 + r)^n − 1) / r)
  where:
• P = future value of the annuity stream
• PMT = payment each period
• r = periodic interest rate (decimal)

• n = number of periods

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• Future value of an annuity due:
  P_due = PMT × (((1 + r)^n − 1) / r) × (1 + r)
  (Multiply the ordinary-annuity result by (1 + r) to account for payments made at the beginning of each period.)

Example

Investing $125,000 at the end of each year for 5 years at 8% (ordinary annuity):

1. Compute the factor: ((1.08^5 − 1) / 0.08) = 5.86660096
2. FV = $125,000 × 5.86660096 ≈ $733,325

If payments are made at the beginning of each year (annuity due), multiply by (1 + r):

FV_due = $733,325 × 1.08 ≈ $791,991

In this example, the annuity due yields $58,666 more because each payment compounds for one additional period.

Future value factor

The future value factor is the multiplier that converts present cash flows into their future value at a given rate and time. For a lump sum, FV factor = (1 + r)^n. For an annuity, the factor is ((1 + r)^n − 1) / r (and times (1 + r) for an annuity due).

Relationship to present value

Present value (PV) and future value are two sides of the same concept: PV discounts future cash flows back to today; FV compounds present or periodic cash flows forward. Knowing any three of the variables (PMT, r, n, PV/FV) lets you solve for the fourth.

Practical uses

• Retirement planning: estimate how periodic contributions accumulate.
• Loan planning: understand how payments grow or how much must be invested to reach a target.
• Comparing payment timing: determine the value difference between beginning- and end-of-period payments.

Key takeaways

• Use P = PMT × (((1 + r)^n − 1) / r) for ordinary annuities; multiply by (1 + r) for annuities due.
• Annuities due always have a higher FV than ordinary annuities, all else equal.
• FV calculations hinge on payment amount, rate of return, and number of periods; small changes in rate or timing can have a large impact due to compounding.

Understanding the future value of an annuity helps you plan contributions and compare different payment schedules to reach financial goals.