Annuity Formula
Calculate the present and future value of regular payments.
Used for retirement planning and loan analysis.
The Formulas
Present Value of Annuity: PV = PMT × [1 - (1+r)⁻ⁿ] / r
An annuity is a series of equal payments made at regular intervals. These formulas let you calculate either how much those payments are worth today (PV) or how much they will grow to in the future (FV).
Variables
| Symbol | Meaning |
|---|---|
| FV | Future value (total accumulated) |
| PV | Present value (lump sum equivalent today) |
| PMT | Payment amount per period |
| r | Interest rate per period |
| n | Total number of payment periods |
Example 1
You invest $500/month for 20 years at 7% annual return. What is the future value?
r = 0.07/12 = 0.005833, n = 20 × 12 = 240
FV = 500 × [(1.005833)²⁴⁰ - 1] / 0.005833
= 500 × [4.0387 - 1] / 0.005833
= $260,464 (you invested $120,000 — earned $140,464 in interest)
Example 2
What is a pension of $2,000/month for 25 years worth today at 5% discount rate?
r = 0.05/12 = 0.004167, n = 25 × 12 = 300
PV = 2000 × [1 - (1.004167)⁻³⁰⁰] / 0.004167
= $342,087 (the lump-sum equivalent today)
When to Use It
Use the annuity formula when:
- Planning retirement savings (how much will monthly contributions grow to?)
- Valuing a pension or structured settlement
- Calculating loan payments (PV annuity)
- Comparing lump-sum vs. periodic payment options