Annuity Calculator

How to use this calculator

1. Enter or choose payment per period.
2. Enter or choose payments per year.
3. Enter or choose interest rate (per year).
4. Enter or choose years.
5. Enter or choose payments made at.
6. The future value updates as you type. Use Copy result or Share to keep it.

Method

FV = P(1 + i)^n + PMT × ((1 + i)^n − 1) ÷ i × (1 + i if paid at the start); PV = PMT × (1 − (1 + i)^−n) ÷ i × (1 + i if paid at the start)

PMT

payment per period

i

annual rate ÷ payments per year

n

years × payments per year

P

starting balance

Worked example

1. i = 5% ÷ 1 = 0.05; n = 10.
2. FV = 1,000 × (1.05^10 − 1) ÷ 0.05 = 1,000 × 12.5779 = 12,577.89.
3. PV = 1,000 × (1 − 1.05^−10) ÷ 0.05 = 1,000 × 7.7217 = 7,721.73.

Ten yearly payments of $1,000 at 5% grow to $12,577.89; the same payments are worth $7,721.73 today.

What the result means

Use the future value for saving towards a goal and the present value to price a stream of payments, such as a structured settlement or a lease. Payments at the start of each period (an annuity due) earn one extra period of interest, so both values are higher by a factor of (1 + i).

Assumptions and limits

• The rate is constant and compounds once per payment period.
• All payments are the same size.
• Insurance-company annuity products have fees, surrender charges and guarantees that this calculation does not include.
• Taxes and inflation are not deducted.