Estimate the future value of regular contributions growing at a fixed annual return.
This tool provides estimates for informational purposes only. It is not a substitute for professional advice. Individual results vary based on your inputs and assumptions, so review important decisions with a qualified professional.
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An annuity is a series of equal payments made at regular intervals over a specified period. The concept underpins mortgages, car loans, pension income, lottery payments, insurance premiums, and countless other financial products. Understanding the mathematics of annuities — and how to calculate present value, future value, and payment amounts — is essential for making sound financial decisions in both everyday life and retirement planning.
In its broadest mathematical sense, an annuity is simply a stream of regular payments. In everyday financial language, an annuity is most commonly a financial product that provides a guaranteed income for life or a fixed period, typically purchased at retirement using a pension pot. The UK annuity market and US annuity market both use this term, though the regulatory frameworks and product structures differ considerably.
The present value (PV) of an annuity tells you how much a series of future payments is worth today, given a specific interest rate. The formula is:
PV = PMT × [1 − (1 + r)^−n] ÷ r
Where: PMT = payment per period; r = interest rate per period; n = number of periods.
Example: You will receive £500/month for 10 years. With a 5% annual interest rate (0.4167%/month), the present value is:
PV = £500 × [1 − (1.004167)^−120] ÷ 0.004167 = £500 × 94.28 = £47,140
This means receiving £500/month for 10 years at 5% annual interest is worth approximately £47,140 today — you would be indifferent between receiving £47,140 now or £500/month for 10 years.
The future value (FV) calculates what a series of regular payments will grow to by the end of the period:
FV = PMT × [(1 + r)^n − 1] ÷ r
Example: You save £200/month for 30 years at 6% annual interest (0.5%/month):
FV = £200 × [(1.005)^360 − 1] ÷ 0.005 = £200 × 1,004.52 = £200,904
This future value formula is the basis of pension pot projection calculators — it shows how regular contributions compound over time.
An ordinary annuity (or annuity in arrears) makes payments at the end of each period. Most loans and mortgages use this structure — you make your first payment one month after borrowing.
An annuity due makes payments at the beginning of each period. Rent and insurance premiums are typically paid in advance (annuity due). Annuity due values are higher than ordinary annuity by a factor of (1 + r):
FV (annuity due) = FV (ordinary) × (1 + r)
Provides a guaranteed fixed payment for a specified period or for life. The insurer takes on investment risk. In the UK, these are the most common type of pension annuity. In the US, fixed annuities are used both for accumulation and income phases.
Payments vary based on the performance of underlying investment sub-accounts (similar to mutual funds). The annuity holder takes on investment risk in exchange for potentially higher returns. Variable annuities are more common in the US than the UK. They often carry high fees (1.5–3% annually) that significantly erode returns.
Returns are linked to a market index (e.g. S&P 500) but typically have a floor (minimum return, often 0%) and a cap or participation rate limiting upside. These products offer a middle ground between fixed and variable.
An immediate annuity starts paying income straight away — typically purchased with a lump sum at retirement. A deferred annuity accumulates value during a savings phase before converting to income at a future date.
Before April 2015, most UK defined contribution pension holders were effectively required to purchase an annuity at retirement — taking a regular income rather than a lump sum. The Pension Freedoms legislation (Finance Act 2014, effective April 2015) removed this obligation. Now, retirees can take their entire pension pot as a lump sum, enter drawdown (leaving the pot invested and drawing as needed), purchase an annuity, or any combination.
As a result, annuity purchases collapsed by approximately 75% in the year following pension freedoms. However, as the cohort of freedom-era retirees has aged, annuity purchases have been recovering — particularly as gilt yields (which drive annuity rates) rose sharply from 2022 onwards. By 2023–24, annuity rates returned to their best levels in over a decade.
UK annuity rates are primarily driven by gilt (government bond) yields and the annuitant's age and health. Typical 2024 rates for a £100,000 pension pot:
| Age at Purchase | Single Life Level (no inflation) | Inflation-linked (RPI) |
|---|---|---|
| 60 | ~£5,800/year | ~£3,600/year |
| 65 | ~£6,500/year | ~£4,200/year |
| 70 | ~£7,800/year | ~£5,100/year |
| 75 | ~£9,500/year | ~£6,300/year |
Enhanced annuities are available for those with health conditions or lifestyle factors (smoking, obesity, diabetes) that reduce life expectancy — these can pay 10–30% more than standard rates.
In the UK, annuity income is taxed as pension income (PAYE). The first 25% of your pension pot can typically be taken as a tax-free lump sum (Pension Commencement Lump Sum); income from the remaining 75% is fully taxable as income.
In the US, the tax treatment depends on whether the annuity was purchased with pre-tax or after-tax money. Annuities within a traditional IRA or 401(k) are fully taxable. Annuities purchased with after-tax money use the "exclusion ratio" — a portion of each payment representing return of cost basis is excluded from tax, and only the earnings portion is taxable.
A joint life annuity continues to pay income (typically 50% or 66%) to the surviving spouse after the annuitant's death. This reduces the initial payment but provides important protection for couples. Inflation-linked annuities (or "escalating annuities") increase payments annually in line with RPI, CPI, or at a fixed rate (e.g. 3%). The trade-off is a much lower initial payment — typically 35–45% less than a level annuity — though the inflation-linked version overtakes the level annuity after approximately 10–15 years of inflation.
PV = PMT × [1 − (1 + r)^−n] ÷ r. Where PMT is the payment per period, r is the interest rate per period, and n is the number of periods. This formula gives the lump-sum equivalent today of a series of future payments.
FV = PMT × [(1 + r)^n − 1] ÷ r. This calculates the total accumulated value of regular payments over time with compound interest. For example, £200/month for 30 years at 6% annual interest grows to approximately £200,904.
An ordinary annuity makes payments at the end of each period (like most mortgages and loans). An annuity due makes payments at the beginning of each period (like rent). Annuity due values are higher by a factor of (1 + r) because payments are received one period earlier.
No. Since the Pension Freedoms legislation took effect in April 2015, UK pension holders are no longer required to purchase an annuity. You can take the pot as a lump sum (all taxable except the 25% tax-free portion), enter drawdown, buy an annuity, or combine these options.
A 65-year-old buying a single life level (no inflation protection) annuity with £100,000 can expect approximately £6,500/year in 2024, based on current gilt yields. Enhanced (impaired life) annuities pay more — potentially £7,000–£9,000+ for those with qualifying health conditions.
Yes. Annuity income from a pension is taxed as income through PAYE. The 25% tax-free lump sum allowance applies to the pension pot — income from the remaining 75% is fully subject to income tax at your marginal rate.
UK annuity rates are primarily driven by gilt (government bond) yields, which represent the insurer's investment return. When gilt yields rise (as they did sharply in 2022–2023), annuity rates improve. Age, gender (for new policies — the ECJ banned gender pricing in 2012, but it is phased out), and health status also affect rates.
An enhanced annuity (also called an impaired life annuity) pays higher income to people with health conditions or lifestyle factors that reduce life expectancy — such as diabetes, cancer, heart disease, or being a smoker. Enhanced rates can be 10–30% higher than standard rates. Always disclose health information to get the best possible rate.