Annuity (payment stream)
Also called Ordinary annuity, Level payment stream
In finance math, a series of equal payments made at regular intervals for a set number of periods.
What it means
In time-value-of-money terms, an annuity is any stream of equal payments spaced evenly over time: monthly loan payments, regular deposits into savings, or fixed pension checks. When payments happen at the end of each period it is an ordinary annuity; when they happen at the start, it is an annuity due.
Formulas let you find the present value of a payment stream (what it is worth as a lump sum today), its future value (what regular deposits grow to), or the payment needed to repay a loan. This concept is distinct from the insurance product also called an annuity, though that product often pays out in this way.
Formula
PV = PMT × (1 − (1 + r)^(−n)) ÷ r
- PV = present value of the payment stream
- PMT = payment each period
- r = rate per period
- n = number of payments
Example
Suppose you will receive $1,000 at the end of each year for 10 years and money earns 5%. The stream is worth about $7,722 today. Going the other way, depositing $500 a month for 20 years at 6% compounded monthly grows to about $231,020, from $120,000 of deposits.
How it’s used
- Comparing a lump sum with installment payments
- Calculating loan and mortgage payments
- Estimating what regular retirement contributions will grow to
Related terms
Educational information only, not financial, tax or legal advice. Rules, limits and rates change; check the IRS, your lender or plan, or a qualified professional before acting.