Annuity Calculator
Calculate the present and future value of any annuity payment stream.
Annuity inputs
Model recurring payments, interest, and timing in one place.
The same payment made each period. 0 is allowed.
The rate for one payment interval, applied as entered. It is not converted from an annual rate.
A whole number of payments, one per period.
Each period is one payment interval. Enter the rate for that interval: an annual rate for annual payments, a monthly rate for monthly payments.
Payment timing
Present value £1,246,221.03, future value £3,306,595.41, for 20 periods of £100,000.00 at 5% per period with end-of-period payments.
Present value (PV)
£1,246,221.03
What this payment stream is worth today at the rate per period.
Future value (FV)
£3,306,595.41
What the payments accumulate to at the end of the final period.
Total payments
£2,000,000.00
£100,000.00 × 20 periods
Interest earned
£1,306,595.41
Future value minus total payments. Negative when the rate is negative.
Payment timing
End
Ordinary annuity
Growth multiple
1.65×
Future value divided by total payments.
Scope
What this calculator assumes
Level payments, fixed rate
Every payment is the same amount, made once per period, and earns or is discounted at one constant interest rate per period.
What is excluded
Taxes, inflation, fees, changing payments, an initial lump sum and conversion between annual and monthly rates are not included.
Planning focused
Use the results to compare payment streams, savings goals, income options and the effect of payment timing.
Interpretation
What these annuity results mean
Future value projection
At 5% per period over 20 periods, £100,000.00 payments accumulate to approximately £3,306,595.41.
Growth multiple
Your future value is about 1.65× your total payments, before taxes, fees and inflation.
Payment timing effect
Paying at the beginning of each period instead would add £62,311.05 on present value and £165,329.77 on future value, because each payment would earn one extra period of interest at a positive rate.
Rate sensitivity
Small changes in the rate per period can significantly affect annuity value, especially when the number of periods is high.
Interest rate
Choosing the interest rate per period
The calculator applies the rate you enter once per payment period and does not convert it. The rate and the number of periods must describe the same interval.
For annual payments, enter an annual rate and the number of years. For monthly payments, enter a monthly rate and the number of months. A 6% nominal annual rate compounded monthly is 6% ÷ 12 = 0.5% per month. A 6% effective annual rate is (1.06)1/12 − 1 ≈ 0.4868% per month. The two give different results, so check which kind of rate you have before converting.
Annuity basics
How annuities work
Recurring payments
An annuity is built from equal payments made on a steady schedule, such as yearly deposits or monthly income.
Interest compounding
Each payment can earn interest, and earlier payments usually have more time to grow.
Time value of money
Money today and money later are not equal when interest, inflation, and opportunity cost matter.
Planning value
Annuity math helps compare savings plans, pension streams, settlement offers, and retirement income.
Assumptions matter
Results depend on payment timing, rate, period count, taxes, fees, and whether payments change over time.
Payment timing
Ordinary annuity vs annuity due
Ordinary annuity
End of period
Each payment is made at the end of its period, as with most loan repayments and many regular savings plans.
Annuity due
Beginning of period
Each payment is made at the start of its period, as with rent or insurance premiums. The result equals the ordinary-annuity value × (1 + r).
PV vs FV
Present value vs future value
Present value
Present value is the single amount today that is equivalent to the whole payment stream, with each payment discounted back at the rate per period.
Future value
Future value is the accumulated amount at the end of the final period, with each payment growing at the rate per period until then.
Formula
Annuity formula explanation
Future value
FV = PMT × [((1 + r)^n − 1) / r]Ordinary annuity. PMT is the payment per period, r the rate per period as a decimal and n the number of periods. At r = 0, FV = PMT × n.
Present value
PV = PMT × [(1 − (1 + r)^−n) / r]Ordinary annuity. Each payment is discounted back to today at the rate per period. At r = 0, PV = PMT × n.
Annuity due
Ordinary annuity result × (1 + r)Payments are made one period earlier. This raises the value when r is positive, leaves it unchanged at 0% and lowers it when r is negative.
Example
Worked example
£1,000 is paid at the end of each period for 10 periods at 5% per period. The 5% is the rate for one payment interval, which is an annual rate only if the payments are annual.
- Present value: 1,000 × (1 − 1.05−10) ÷ 0.05 ≈ £7,721.73
- Future value: 1,000 × (1.0510 − 1) ÷ 0.05 ≈ £12,577.89
- Total payments: 1,000 × 10 = £10,000.00
- Interest earned: £12,577.89 − £10,000.00 ≈ £2,577.89
FAQ
Annuity calculator questions
Estimate only. This calculator is for general planning and education, not financial, tax, investment, legal, lender, or professional advice. Compounding examples are estimates. Actual rates, terms, fees, taxes, and withdrawal rules can vary by account or provider. Verify important decisions with a qualified professional, lender, official source, or relevant institution.