What Is an Annuity?
An annuity is a series of equal payments made at regular intervals over a fixed period. Annuities appear in many financial contexts: mortgage and loan repayments are annuities paid to the lender; retirement income products pay annuities to retirees; and pension plans, structured settlements, and lease payments all follow the annuity structure. Understanding annuity math lets you evaluate any stream of regular payments on an apples-to-apples basis.
Two values define every annuity's worth: its present value (PV) — the lump sum today that is equivalent to the entire payment stream — and its future value (FV) — how much those payments will accumulate to if invested at the stated rate. Lenders use PV to price loans; investors use FV to project wealth accumulation.
Ordinary Annuity vs. Annuity Due
The timing of payments creates two distinct types:
- Ordinary annuity (annuity in arrears): Payments occur at the end of each period. This is the standard for most loans (your mortgage payment is due at month-end) and most financial calculators.
- Annuity due: Payments occur at the beginning of each period. Rent, insurance premiums, and lease payments are common examples — you pay before receiving the benefit. Because each payment is made one period earlier, an annuity due is worth slightly more than an ordinary annuity at the same rate. The calculator multiplies both PV and FV by (1 + r) to reflect this.
Present Value of an Annuity Explained
The present value tells you what a future stream of payments is worth right now, discounted at a given interest rate. This concept is the foundation of loan pricing: a lender calculates the PV of your scheduled repayments and offers you that amount today. If you're evaluating a structured settlement or pension buyout offer, comparing the lump-sum offer to the PV of the payment stream (at a reasonable discount rate) tells you whether you're getting a fair deal.
PV decreases as the discount rate rises — higher interest rates make future payments worth less today. This is why bond prices fall when interest rates rise: the fixed coupon payments are discounted at a higher rate, reducing present value.
Future Value of an Annuity Explained
The future value shows how much your regular contributions will accumulate to over time, assuming they earn the stated rate. This is the core calculation behind retirement planning: if you contribute $500/month for 30 years at 7% annual return, the FV tells you your ending account balance. The growth comes from two sources — your contributions and the compounding returns they earn. In the early years, contributions dominate; in later years, investment returns overtake them dramatically.
How to Use This Annuity Calculator
- Payment amount: The fixed payment per period. For savings/investment analysis, this is your regular contribution. For loan analysis, this is your regular payment.
- Annual interest rate: The growth rate (for savings) or discount rate (for PV analysis). Use expected market returns for retirement projections; use the loan rate for debt analysis.
- Number of years: The total duration. The calculator computes total periods based on years × frequency.
- Payment frequency: Monthly is standard for most loans and savings plans; quarterly and annual suit pension analysis.
- Annuity type: Choose ordinary (most loans) or due (rent, insurance, leases).
Common Annuity Applications
- Retirement planning: Use FV to project how regular 401(k) contributions will grow to a target nest egg by retirement age.
- Mortgage analysis: Use PV to verify that your loan amount equals the PV of your monthly payments — a quick sanity check on any loan offer.
- Pension buyout evaluation: Compare a lump-sum buyout offer to the PV of the remaining pension payments at your personal discount rate.
- Structured settlements: Calculate whether accepting a lump sum or keeping the payment stream provides more value at a given assumed investment return.