Future Value Calculator

Background.

Put $1,000 away at 7% a year and leave it for a decade, and it comes back as $1,967.15: almost double, with $967.15 of that earned rather than deposited. That figure is a future value, the amount money grows to when it earns a steady rate and the interest stays in the account to earn interest of its own.

Most savings plans have two parts, and the formula used here handles both at once. A lump sum already invested grows as PV × (1 + i)ⁿ. A run of equal deposits, such as $200 a month into a retirement account, is an annuity, and each deposit compounds for a different length of time: the first for nearly the whole term, the last for a single period or none at all. Add the two pieces and you have the balance at the end.

The inputs are the ones a financial calculator uses. The rate is the nominal annual rate, divided by the compounding frequency to give the rate per period, and the years are multiplied by the same frequency to count the periods. The payment is made once per compounding period, so monthly compounding means monthly deposits and annual compounding means one deposit a year. Deposits can land at the end of each period, as they do in most savings plans, or at the start, which gives each one an extra period of interest.

Switch the Solve For setting and the same equation runs backwards, telling you how much to invest today, how much to deposit each period or how many years a target will take. Every answer is in nominal dollars at a rate that never changes, before tax, fees and inflation.

What is future value calculator?

Future value is the amount that a present sum, a series of regular payments, or both will have grown to after a set number of compounding periods at a constant rate of return. It is the forward half of the time value of money, the principle that a dollar available now is worth more than a dollar promised later because the earlier dollar can be invested in the meantime; present value runs the same relationship in reverse. Two rate measures sit behind it. The nominal annual rate, or APR, is the quoted figure before compounding. The effective annual rate is what a year of compounding actually delivers. It is the same idea as the APY that US banks disclose on deposit accounts under the Truth in Savings rules (Regulation DD), while lenders quote an APR under Truth in Lending (Regulation Z).

How to use this calculator.

1. 01Choose what to Solve For. Future Value projects forward; Present Value, Payment and Years work backwards from a goal you type into Target Future Value, which is ignored in forward mode.
2. 02Enter the starting balance as Present Value and the regular deposit as Periodic Payment. Use 0 for whichever you do not have: no payment for a single lump sum, no present value for a plan that starts from nothing.
3. 03Type the Annual Interest Rate as a nominal rate and pick the Compounding Frequency that matches how often you deposit, because one payment is made per period. If your account quotes an APY, convert it first: 4.5% APY compounded monthly is a nominal 4.41%.
4. 04Set Years and Payment Timing. End of Period fits deposits made after each pay cycle; Beginning of Period fits money paid in advance, such as rent, lease payments or insurance premiums.
5. 05Read the results. In the backward modes the Future Value shown is simply your target, and the unknown you solved for appears in its own row: Present Value, Periodic Payment or Years. If the other inputs already reach the target, the calculator says so instead of showing a negative answer.

The formula.

The balance is the sum of two growth terms: FV = PV(1 + i)ⁿ + PMT × [(1 + i)ⁿ − 1] ÷ i, where i is the rate per period (annual rate ÷ 100 ÷ compounding frequency) and n is the number of periods (years × compounding frequency).

The first term compounds a single deposit. Each period multiplies it by 1 + i, so after n periods it has been multiplied by (1 + i)ⁿ; at 7% a year for ten years that factor is 1.9672.

The second term adds up the stream of equal payments. With end-of-period timing the first payment compounds for n − 1 periods and the last for none, which makes the stream a geometric series whose sum is PMT × [(1 + i)ⁿ − 1] ÷ i. With Beginning of Period selected every payment arrives one period earlier, so the annuity term is multiplied by (1 + i) while the lump sum is unaffected. At a zero rate the series collapses to PMT × n and the balance is exactly what you paid in.

The effective annual rate, EAR = (1 + i)^m − 1 with m the compounding frequency, shows what frequency does to a nominal rate: 7% becomes 7.1859% compounded quarterly, 7.2290% monthly and 7.2501% daily.

The backward modes rearrange the same equation. Present value is the target minus the payments' future value, discounted by (1 + i)ⁿ. Payment is the gap between the target and the lump sum's growth, divided by the annuity factor. Years comes from logarithms: n = ln[(FV·i + PMT·d) ÷ (PV·i + PMT·d)] ÷ ln(1 + i), where d is 1 for end-of-period payments and 1 + i for beginning-of-period ones, and the answer is n divided by the frequency, so it can be a fraction of a year. A target at or below the starting balance, or a zero rate with no payment, cannot be solved for years and is rejected. When solving for payment or present value, a target the other inputs already overshoot would give a negative answer, so the calculator refuses it and says the target is already met.

Total contributions are PV plus PMT × n, and total interest is the future value minus that sum.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Brealey, R.A., Myers, S.C., and Allen, F. — Principles of Corporate Finance, 13th edition. Chapter 2 introduces the future value identity FV = PV × (1 + r)^t and develops the annuity formulas used in this calculator.
2. [2]Bodie, Z., Kane, A., and Marcus, A.J. — Investments, 12th edition. §5 covers the time value of money, effective vs. nominal rates, and annuity valuation as applied to portfolio choice.
3. [3]CFA Institute — Quantitative Methods curriculum, Time Value of Money reading. Defines FV/PV/PMT/n/i framework and the inverse solvers used at the Level I exam.
4. [4]U.S. Securities and Exchange Commission, Investor.gov — Compound Interest Calculator and accompanying investor-education materials on future value and the time value of money.
5. [5]Mishkin, F.S. — The Economics of Money, Banking, and Financial Markets, 13th edition. Chapter 4 derives the future and present value formulas and motivates the role of compounding frequency in fixed-income pricing.
6. [6]Consumer Financial Protection Bureau — Regulation Z (Truth in Lending) and Regulation DD (Truth in Savings), which mandate APR and APY disclosure so consumers can compare nominal-rate products on an effective-annual-rate basis.