Annuity Calculator
Compute the future value, present value, or periodic payment of an annuity — the textbook time-value-of-money formulas used by Excel's FV(), PV(), and PMT() functions.
Future value
£41,103.37
- Total paid in
- £24,000.00
- Interest earned
- £17,103.37
- Present value equivalent
- £15,152.53
Future value of an ordinary annuity: FVA = PMT · ((1+r)^n − 1) / r, where r is the period rate (annual rate / periods per year) and n is the total number of periods.
How to use this calculator
Pick what you want to solve for at the top. If you choose Future or Present value, enter the regular payment you plan to make or receive. If you choose Payment, enter the starting lump sum you want to convert into a stream of equal payments. Then set the annual interest rate, the term in years, and how often payments occur. Results update as you type.
How the calculation works
The calculator uses the standard ordinary-annuity formulas (payments at the end of each period): FV = PMT · ((1+r)^n − 1) / r for future value, PV = PMT · (1 − (1+r)^-n) / r for present value, and PMT = PV · r / (1 − (1+r)^-n) for the periodic payment that exhausts a present-value lump sum. Here r is the period interest rate (annual rate divided by periods per year) and n is the total number of periods. These match Excel's FV(), PV(), and PMT() with type=0.
Worked example
Future value example: paying $100 a month for 20 years at a 6% nominal annual rate (monthly compounding). Period rate r = 0.06 / 12 = 0.005, periods n = 240. FV = 100 · ((1.005)^240 − 1) / 0.005 ≈ $46,204.09 from $24,000 of contributions, with $22,204.09 of compound interest. Payment example: turning a $100,000 lump sum into 20 annual payments at 5%: PMT = 100,000 · 0.05 / (1 − 1.05^-20) ≈ $8,024.26 per year.
Frequently asked questions
What is an annuity in finance?
In time-value-of-money terms, an annuity is just a series of equal cash flows occurring at regular intervals — monthly pension payments, lease rentals, bond coupon payments, the monthly contribution into a savings account, or the monthly repayment on a mortgage. The "annuity calculator" name is a holdover from insurance-style retirement-income products, but the maths is the same general TVM toolkit that powers loans, savings plans, and pension drawdown.
What is the difference between an ordinary annuity and an annuity due?
Ordinary annuity payments occur at the end of each period (typical for loans, bonds, and most savings plans). Annuity-due payments occur at the start of each period (typical for rents and some insurance products). For the same rate, term, and payment, an annuity due has a future and present value that are larger by a factor of (1 + r). This calculator uses the ordinary-annuity convention — the same default as Excel's FV(), PV(), and PMT() with type=0. To convert any result to annuity-due, multiply by (1 + r), where r is the period rate.
When should I solve for future value vs. present value vs. payment?
Solve for future value when you know what you will contribute each period and want to know what it grows to (savings plan, sinking fund). Solve for present value when you know what you will receive each period and want to know the equivalent lump sum today (pricing a bond coupon stream, valuing a pension). Solve for payment when you know the starting lump sum and want to know how much it pays out per period — the classic retirement-income-from-a-pot question, or equivalently a loan payment.
Does this match what Excel or Google Sheets gives me?
Yes — sign conventions aside. Excel's =FV(rate, nper, pmt) returns a negative result when pmt is positive (and vice versa) because it treats inflows and outflows with opposite signs. This calculator returns positive absolute values. So Excel =FV(0.06/12, 240, -100) ≈ 46,204.09 matches solving for future value with $100 monthly payments. Similarly =PV(0.05, 10, -1000) ≈ 7,721.73 and =PMT(0.05, 20, -100000) ≈ 8,024.26.
What about taxes and inflation?
The result is nominal — the number of dollars (or pounds, euros, etc.) at the end, in current money. To estimate real purchasing power, subtract your expected inflation rate from the rate you enter (a 7% nominal rate with 2% inflation is roughly 5% real). For tax, the calculator assumes growth is sheltered (e.g. inside an IRA, ISA, or pension wrapper). For a taxable account, deduct your marginal rate from each period's interest. Annuity products themselves have specific tax treatment that varies by jurisdiction — this is pure TVM, not product-specific.
Does the rate need to be the nominal rate or the effective rate?
Enter the nominal annual rate — the headline rate most providers quote. The calculator divides it by the number of compounding periods per year to get the period rate, matching the standard convention used in finance textbooks and spreadsheet TVM functions. If a product quotes only an effective annual rate (EAR or APY), you can convert: nominal = m · ((1 + EAR)^(1/m) − 1), where m is periods per year.