Future value calculator

What does a future value calculator work out?

Future value (FV) is what money is worth at a later date once a stated rate has been applied to it for a stated number of periods. This page answers the textbook version of that question: a sum you have now, plus an equal payment every period, growing at one rate. That is the shape of an exam question, a spreadsheet FV function and the TVM keys on a financial calculator, so the three give the same answer here.

Using the default inputs, $10,000 today and $2,000 at the end of each year at 6% reach $44,270.07 after 10 years. The $10,000 on its own becomes $17,908.48; the ten payments together become $26,361.59. You put in $30,000, and growth adds $14,270.07.

If you want deposits that differ in frequency from the compounding, such as monthly saving into an account that compounds daily, or a result adjusted for inflation, the compound interest calculator is built for that. Here every period has one length, and the focus is on annuity timing, factors and the exact keystrokes.

What is the future value formula?

Two parts are added together. For the sum held today: FV = PV x (1 + i)^n. For a level payment made at the end of every period: FV = PMT x ((1 + i)^n - 1) / i. Here i is the rate per period and n the number of periods.

Both come from the annual rate and the years you enter. With yearly periods, i is the annual rate and n the number of years. With monthly periods, i is the annual rate divided by 12 and n is the years times 12, so 5% a year for 15 years becomes 0.4167% a month for 180 months. The bracketed term in the second formula is the annuity factor for future value: the amount that 1 paid each period builds up to.

At a 0% rate both formulas reduce to the money paid in, and the calculator shows exactly that. Open Show the working under the result to see each part with your own numbers.

How do you calculate the future value of an annuity, step by step?

A written answer usually works out each factor, rounds it to three decimals, and multiplies. For the default inputs at 6% over 10 years:

Rounded factors give $44,272, while unrounded ones give $44,270.07, a gap of $1.93. Both appear above: the headline is exact, and the factor table under the calculator reproduces the hand layout for whatever you enter.

A shorter annuity in euros shows the same steps. Paying €1,000 at the end of each year for 5 years at 8% uses a factor of 5.867, so the answer by hand is €5,867; the exact figure is €5,866.60. Of that, €5,000 is your money and €866.60 is growth.

Ordinary annuity or annuity due: what changes?

An ordinary annuity pays at the end of each period, so the final payment earns nothing. An annuity due pays at the start, so every payment, including the last, earns one more period of growth. That makes the annuity due figure the ordinary figure multiplied by (1 + i).

On the default inputs the ten payments grow to $26,361.59 when paid at year ends and to $26,361.59 x 1.06 = $27,943.29 when paid at the start of each year. Adding the $17,908.48 from the lump sum, the total rises from $44,270.07 to $45,851.76, a difference of $1,581.69. The lump sum is unaffected, because it is already invested at the start.

Two hand methods give the annuity due factor: the ordinary factor times (1 + i), 13.181 x 1.06, or the factor for one extra period minus 1, which is 13.972 at 6% for 10 payments. Switch Payments made above to compare, and the second chart shows both totals side by side.

How do you calculate future value in Excel or Google Sheets?

Microsoft documents the function as =FV(rate, nper, pmt, [pv], [type]). Rate is the rate per period, nper the total number of periods, pmt the payment each period, pv the amount today, and type is 0 or omitted for payments at the end of each period and 1 for the start. Microsoft's own rule for signs is that cash you pay out is negative and cash you receive is positive.

So the default example is =FV(6%, 10, -2000, -10000), which returns 44,270.07. Enter the payment and the lump sum as positive numbers and Excel returns -44,270.07: the same size, with the sign telling you it is money coming back to you. Add 1 as the fifth argument, =FV(6%, 10, -2000, -10000, 1), for the annuity due figure of 45,851.76.

Microsoft also warns that rate and nper must use the same period. Its own monthly example, $1,000 a month for 12 months at 12% a year, returns $12,682.50; with the values typed in place of its cell references, that is =FV(12%/12, 12, -1000); enter $1,000, monthly periods, 12% and 1 year above and the calculator agrees. Google Sheets uses the same order, named rate, number_of_periods, payment_amount, present_value and end_or_beginning, with the last two defaulting to 0. The panel under the calculator writes the formula for your inputs.

How do you find future value on a BA II Plus?

The Texas Instruments guidebook describes a TVM worksheet with five variables, N, I/Y, PV, PMT and FV, and two settings: P/Y, payments per year, and C/Y, compounding periods per year. Both default to 1, and the payment setting defaults to END. I/Y is entered as the nominal annual rate, outflows are entered as negative numbers, and entering a value for P/Y also sets C/Y to the same value. The guidebook gives the key sequence for each step.

For the default example, reset the TVM variables, enter 10 for N, 6 for I/Y, -10000 for PV and -2000 for PMT, then compute FV. The display shows 44,270.07. For payments at the start of each period, change the payment setting from END to BGN, which the guidebook names the annuity due case, and compute again.

For monthly payments, set P/Y to 12; N then counts months, while I/Y stays the yearly rate. Saving £250 a month for 15 years at 5% becomes N = 180, I/Y = 5, PV = 0 and PMT = -250; computing FV gives £66,822.24, the same as this calculator. The panel under the result lists these entries for whatever you type.

How does each input change the future value?

The rate and the number of years do most of the work. Holding the other defaults fixed:

Doubling the time from 10 to 20 years more than doubles the answer, because the money paid in rises from $30,000 to $50,000 and every dollar also compounds for longer. The period length matters less: the $10,000 lump sum alone reaches $17,908.48 with yearly compounding and $18,193.97 with monthly compounding over the same 10 years at 6%.

Worked examples in pounds and dirhams

The arithmetic does not change with the currency, and nothing is converted.

• Monthly saving in pounds. £250 at the end of every month for 15 years at 5% a year: 180 payments at 0.4167% a month grow to £66,822.24. You pay in £45,000 and growth adds £21,822.24. Paid at the start of each month, the total is £67,100.66.
• A lump sum in dirhams. AED 50,000 at 4% a year compounded quarterly for 7 years: 28 quarters at 1% each give AED 66,064.55. The effective annual rate is 4.0604%. With yearly compounding the same sum would reach AED 65,796.59.
• Both together. Add AED 1,000 at the end of every quarter to that lump sum and the 7-year total is AED 98,193.65.

Common future value mistakes

• Putting the yearly rate against monthly periods. 6% entered as the rate for 120 monthly periods turns $10,000 into about $10.9 million. Divide the rate by 12 as well.
• Leaving nper in years. 0.5% a month for 10 periods is 10 months, not 10 years, and grows $10,000 only to $10,511.40.
• Mixed signs. In a spreadsheet, a payment entered as negative and a lump sum as positive tells the function that one is paid in and the other taken out, which nets them against each other.
• Forgetting the timing setting. Spreadsheets and the BA II Plus both default to end-of-period payments; annuity due questions need type 1 or BGN.
• Using a 3-decimal factor where precision matters. It is fine for a written answer, but over long periods or large sums the gap from the exact figure grows.

What this calculator leaves out, and a short glossary

It applies one fixed rate to equal payments. It does not cover payments that grow each year, rates that change, tax, fees or withdrawals, and it does not adjust for inflation. Investment returns move from year to year and can be negative, so a rate entered here is an assumption to test, not a promise. For a target figure and a plan to reach it, the savings calculator works backward from the goal.

Future value: what an amount, or a stream of amounts, is worth at a set later date. Present value: the amount today. Annuity: equal payments at equal intervals. Ordinary annuity: payments at the end of each period. Annuity due: payments at the start of each period. Compound factor: (1 + i)^n. Annuity factor (future value): ((1 + i)^n - 1) / i.

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