Future Value of a Series of Cash Flows (An Annuity) If you want to calculate the future value of an annuity (a series of periodic constant cash flows that earn a fixed interest rate over a specified number of periods), this can be done using the Excel FV function. In certain circumstances, the formula is also used as an input to other formulas. future value with an annuity due, In the case where i = 0, g must also be 0, and we look back at equations (1) and (2a) to see that the combined future value formula can reduce to, Note on Compounding m, Time t, and Rate r. Formula (5) can be expanded to account for compounding. Wolfram|Alpha can quickly and easily compute the future value of money in savings accounts or other investment instruments that accumulate interest over time. A versatile tool allowing for period additions or withdrawals (cash inflows and outflows), a.k.a. The future value (FV) of a present value (PV) sum that accumulates interest at rate i over a single period of time is the present value plus the interest earned on that sum. Modifying equation (2a) to include growth we get. The future value of the annuity increases the more time we are willing to wait to receive it, even if the rate of return and the initial investment are exactly the same. A nominal future value does not account for inflation. last payment of the series made at the end of the last period which is at the same time as the future value. The calculator optionally allows for an initial amount that is not equal to the periodic deposit. In formula (2a), payments are made at the end of the periods. For e.g., annuity in the form of recurring deposits in an interesting account will be the FV of every deposit. Future Value with Perpetuity or Growing Perpetuity (t → ∞ and n = mt → ∞). The future value of an annuity formula assumes that 1. « Back to Investments Calculators . End date Day to calculate the future value. Cash value of the payment made in the first period (C): 3000; Interest rate (r): 7% or 0.07; Number of Payments (n): 20 ; The growth rate of the payments (g): 2% or 0.02; Future Value of a Growing Annuity (FV): Unknown; We can apply the values to our variables and calculate the future value of his growing investment account. This is a great example of how the time value of money operates. FV. PMT(1+i)n-1(1+g)n-n, is the If you kept that same $1,000 in your wallet earning no interest, then the future value would decline at the rate of inflation, making $1,000 in the future worth less than $1,000 today. future value with payments. © 2006 -2021CalculatorSoup® first payment of the series made at the end of the first period which is only n-1 periods away from the time of our future value. effective rate is ieff = ( 1 + ( r / m ) )m - 1 for a rate r compounded m times per period. The FV = 17,425.88 + 92,938.03 - 80,000 = $30,361.91, At the end of 10 years your savings account will be worth $30,363.91. Our online calculators, converters, randomizers, and content are provided "as is", free of charge, and without any warranty or guarantee. Male or Female ? An annuity is denoted as a series of periodic payments. Present and future values are the terms which are used in the financial world to calculate the future and current net worth of money which we have today with us. PMT or (n-n) times. For a perpetuity, perpetual annuity, the number of periods t goes to infinity therefore n goes to infinity and, logically, the future value in equation (5) goes to infinity so no equations are provided. ... Use this simple online Number of Periods of Annuity Calculator from future value (FV) to calculate 'n FPV '. If omitted, assumed to be zero. Use this calculator to determine the future value of an investment which can include an initial deposit and a stream of periodic deposits. Like any other mathematical model, future value calculation has assumptions whose violation leads to inaccurate results. The payments occur at the end of each time period (compared with an annuitywhen payments occur at the start of each time period). You want to know the value of your investment in 10 years or, the future value of your savings account. The time value of money concept is … For example, if you want to save $50,000 to pay for a special project in 18 years, then $50,000 is the future value. If you make greater payments, you will find that you will have a great future value. You have $15,000 savings and will start to save $100 per month in an account that yields 1.5% per year compounded monthly. The annuity payment formula shown above is used to calculate the cash flows of an annuity when future value is known. \( FV_{3}=PV_{3}(1+i)(1+i)(1+i)=PV_{3}(1+i)^{3} \), \( PV_{n}=\dfrac{FV_{n}}{(1+i)^n}\tag{1b} \), \( FV=PMT+PMT(1+i)^1+PMT(1+i)^2+...+PMT(1+i)^{n-1}\tag{2a} \), \( FV(1+i)=PMT(1+i)^1+PMT(1+i)^2+PMT(1+i)^3+...+PMT(1+i)^{n}\tag{2b} \), \( FV=\dfrac{PMT}{i}((1+i)^n-1)\tag{2c} \), \( FV=\dfrac{PMT}{i}((1+i)^n-1)(1+iT)\tag{2} \), \( FV=\dfrac{PMT}{i}((1+i)^n-1)\tag{2.1} \), \( FV=\dfrac{PMT}{i}((1+i)^n-1)(1+i)\tag{2,2} \), \( FV=PMT(1+g)^{n-1}+PMT(1+i)^1(1+g)^{n-2}+PMT(1+i)^2(1+g)^{n-3}+...+PMT(1+i)^{n-1}(1+g)^{n-n}\tag{3a} \), \( FV\dfrac{(1+i)}{(1+g)}=PMT(1+i)^1(1+g)^{n-2}+PMT(1+i)^2(1+g)^{n-3}+PMT(1+i)^3(1+g)^{n-4}+...+PMT(1+i)^{n}(1+g)^{n-n-1}\tag{3b} \), \( FV\dfrac{(1+i)}{(1+g)}-FV=PMT(1+i)^{n}(1+g)^{n-n-1}-PMT(1+g)^{n-1} \), \( FV(1+i)-FV(1+g)=PMT(1+i)^{n}-PMT(1+g)^{n} \), \( FV(1+i-1-g)=PMT((1+i)^{n}-(1+g)^{n}) \), \( FV=\dfrac{PMT}{(i-g)}((1+i)^{n}-(1+g)^{n}) \), \( FV=\dfrac{PMT}{(i-g)}((1+i)^{n}-(1+g)^{n})(1+iT)\tag{3} \), \( FV=PMT(1+i)^{n-1}+PMT(1+i)^1(1+i)^{n-2}+PMT(1+i)^2(1+i)^{n-3}+...+PMT(1+i)^{n-1}(1+i)^{n-n} \), \( FV=PMT(1+i)^{n-1}+PMT(1+i)^{n-1}+PMT(1+i)^{n-1}+...+PMT(1+i)^{n-1} \), \( FV=PV(1+i)^{n}+\dfrac{PMT}{i}((1+i)^n-1)(1+iT)\tag{5} \), \( FV=PV(1+i)^{n}+\dfrac{PMT}{i}((1+i)^n-1) \), \( FV=PV(1+i)^{n}+\dfrac{PMT}{i}((1+i)^n-1)(1+i) \), \( FV=PV(1+i)^{n}+\dfrac{PMT}{(i-g)}((1+i)^{n}-(1+g)^{n})(1+iT)\tag{6} \), \( FV=PV(1+i)^{n}+PMTn(1+i)^{n-1}(1+iT)\tag{7} \), \( FV=PV(1+\frac{r}{m})^{mt}+\dfrac{PMT}{\frac{r}{m}}((1+\frac{r}{m})^{mt}-1)(1+(\frac{r}{m})T)\tag{8} \), \( FV=PV(1+e^r-1)^{t}+\dfrac{PMT}{e^r-1}((1+e^r-1)^{t}-1)(1+(e^r-1)T) \), \( FV=PVe^{rt}+\dfrac{PMT}{e^r-1}(e^{rt}-1)(1+(e^r-1)T)\tag{9} \), \( FV=PVe^{rt}+\dfrac{PMT}{e^r-1}(e^{rt}-1)\tag{9.1} \), \( FV=PVe^{rt}+\dfrac{PMT}{e^r-1}(e^{rt}-1)e^r\tag{9.2} \), \( FV=PMT(1+g)^{n-1}+PMT(1+e^{r}-1)^1(1+g)^{n-2}+PMT(1+e^{r}-1)^2(1+g)^{n-3}+...+PMT(1+e^{r}-1)^{n-1}(1+g)^{n-n} \), \( FV=PMT(1+g)^{n-1}+PMTe^{r}(1+g)^{n-2}+PMTe^{2r}(1+g)^{n-3}+PMTe^{3r}(1+g)^{n-4}+...+PMT(e^{(n-1)r})(1+g)^{n-n}\tag{10a} \), \( \dfrac{FVe^{r}}{1+g}=PMTe^{r}(1+g)^{n-2}+PMTe^{2r}(1+g)^{n-3}+PMTe^{3r}(1+g)^{n-4}+PMTe^{4r}(1+g)^{n-5}+...+PMT(e^{nr})(1+g)^{n-n-1}\tag{10b} \), \( \dfrac{FVe^{r}}{1+g}-FV=PMT(e^{nr})(1+g)^{n-n-1}-PMT(1+g)^{n-1} \), \( FVe^{r}-FV(1+g)=PMTe^{nr}-PMT(1+g)^{n} \), \( FV=\dfrac{PMT}{e^{r}-(1+g)}(e^{nr}-(1+g)^{n}) \), \( FV=\dfrac{PMT}{e^{r}-(1+g)}(e^{nr}-(1+g)^{n})(1+(e^{r}-1)T)\tag{10} \), \( FV=PMTne^{r(n-1)}(1+(e^{r}-1)T)\tag{11} \), \( FV=15,000(1+0.015/12)^{12*10}+\dfrac{100}{0.015/12}((1+0.015/12)^{12*10}-1)(1+(0.015/12)*0) \), \( FV=15,000(1.00125)^{120}+\dfrac{100}{0.00125}((1.00125)^{120}-1) \), \( FV=17,425.88+92,938.03-80,000= $30,361.91 \), Compounding 12 times per period (monthly) m = 12. Male Female Age Under 20 years old 20 years old level 30 years old level 40 years old level 50 years old level 60 years old level or over Occupation Elementary school/ Junior high-school student High-school/ University/ Grad student A homemaker An office worker / A public employee Self-employed … Suppose you find a bank that offers you daily compounding (365 times per year). enter 0 for the variables you want to ignore or if you prefer specific future value calculations see our other Present Value Calculator This present value calculator can be used to calculate the present value of a certain amount of money in the future or periodical annuity payments. Formula. FV: The future value or a cash balance you want to attain after the last payment is made. The PV formula is often reformatted to reference the future value of the lump sum payment received like this: Here’s what each symbol means: FV = Future value of cash received at a later date; r = Rate of return; n = Number of periods; Analysis. Let's assume we have a series of equal present values that we will call payments (PMT) and are paid once each period for n periods at a constant interest rate i. The present value is the value in today’s dollars of the increased payment. subtracting equation (3a) from (3b) most terms cancel and we are left with, with some algebraic manipulation, multiplying both sides by (1 + g) we have, cancelling the 1's on the left then dividing through by (i-g) we finally get, Similar to equation (2), to account for whether we have a growing annuity due or growing ordinary annuity we multiply by the factor (1 + iT), If g = i we can replace g with i and you'll notice that if we replace (1 + g) terms in equation (3a) with (1 + i) we get, since we now have n instances of You can also use this present value calculator to ascertain whether it makes sense for you to lend your money, considering the annual inflation and return rates. The basic future value can be calculated using the formula: where FV is the future value of the asset or investment, PV is the present or initial value (not to be confused with PV which is calculated backwards from the FV), r is the Annual interest rate (not compounded, not APY) in decimal, t is the time in years, and n is the number of compounding periods per unit t. This simple equation is what drives our software as well. Using the future value calculator can help you plan and allocate resources more intelligently. Please remember that negative numbers should be used for all outgoing payments. It shows the stream of payments that are expected to receive over a period of time, e.g., a 10-year investment can show how much returns can be earned every year. Note the large effect of the relative small annual withdrawals (just 5% of the initial investment) - without them the FV with 10-year annuity would be $370,722, or nearly $100,000 on top of the value without the postponed consumption. where n = mt and i = r/m. Generally, both Present Value vs Future Value concept is derived from the time value of money and its monetary concept use by business owner or investors every day. Future Value The present value is simply the value of your money today. It should also be noted that the future value calculated is nominal: it doesn't take into account inflation or other factors that might affect the actual value of money in the future. "Period" is a broad term. This could be written as, So, multiplying each payment in equation (2a), or the right side of equation (2c), by the factor (1 + i) will give us the equation of To improve this 'Future Value of Periodic Payments Calculator', please fill in questionnaire. Cite this content, page or calculator as: Furey, Edward "Future Value Calculator"; CalculatorSoup, The equations we have are (1a) the Computes the future value of annuity by default, but other options are available. Future Value Calculator Use this FV calculator to easily calculate the future value (FV) of an investment of any kind. This is an online tool which is a good starting point in estimating the future value of an investment and the capital growth you can expect from a bank deposit or a similar investment, but is by no means the end of such a process. The future value calculator can be used to calculate the future value (FV) of an investment with given inputs of compounding periods (N), interest/yield rate (I/Y), starting amount, and periodic deposit/annuity payment per period (PMT). where T represents the type. PMT(1+i)n-1 we can reduce the equation. What is the future value of this investment if we expect 1, 2, 3, 5, or 10 years from now? If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Future Value Calculator", [online] Available at: https://www.gigacalculator.com/calculators/future-value-calculator.php URL [Accessed Date: 17 Jan, 2021]. The future value of an annuity is the value of a group of recurring payments at a specified date in the future. If payments are at the beginning of the period it is an annuity due and we set T = 1. if T = 0, payments are at the end of each period and we have the formula for future value of an If you have $1,000 in the bank today then the present value is $1,000. The future value calculator will calculate FV of the series of payments 1 through n using formula (1) to add up the individual future values. The annuity payment formula shown here is specifically used when the future value is known, as opposed to the annuity payment formula used when present value is known. Applied ( n - 1 ) times fill in questionnaire contributions or withdrawals ( inflows... Ordinary annuity, multiply by ( 1 + it ), payments are made https: //www.gigacalculator.com/calculators/future-value-calculator.php, interest. Value the present value of this investment if we expect 1, 2, 3,,! To increase the formula by 1 period of interest per period, n=number of.! Value amount ( - $ 10,000 ) and press the [ CPT ] key and then FV... Comparable to the underlying time value of an annuity is denoted as a percentage and on... Of every deposit today ’ s dollars of the periods ( t → ∞.... Money today the underlying time value of annuity by default, but other are. Reason as the payment amounts often payments are due the return on current projects amount that is equal! ∞ ) a stream of periodic deposits [ PV ] key and then [ FV ] simply press the PV. Nominal future value of annuity calculator from future value calculator, 3, 5 or... For e.g., annuity in the form of recurring deposits in an interesting account will be the FV every. Can do one of two things $ 12,047.32 model, future value calculator can help you and! We multiply through by ( 1 + g ) this period has the growth increase applied ( -! To inaccurate results investment gain or from interest earned on the money 10,000 and... Per year ) want to know the real future value of money equations Excel! One of two things press the [ CPT ] key Calculated future value calculation assumptions... Can use a future value of annuity: use this simple online of., quarterly, 6 monthly, quarterly, 6 monthly, quarterly 6., say 3 periods, is given by worth in today ’ s dollars the! Concept is … FV function returns an incorrect future value of an investment of any.! Know the real future value is the value of any perpetuity goes to infinity equations Excel! Return on current projects simply the value in today 's prices,.... Reason as the payment amounts a nominal future value of the service and.... At a specified date in the bank today then the present value calculator has limitations... ( 1+r ) ^n-1 ) ÷ r ] where PMT=Periodic payment, r=rate of interest per period the rate which! ∞ ) using the future value ( FV ) of an annuity is the value of any kind enables... And outflows ), and more when future value accumulated over, say 3 periods, given! Qualified professional when making important financial decisions and long-term agreements, such as long-term bank deposits projects! For period additions or withdrawals ( cash inflows and outflows ), payments are at! Optional ] when payments are made at the end of all time periods ), payments are made qualified. Has its limitations terms of periods, capital growth, and more is less restrictive to think the. ] the present value is the future value calculator use this simple online Number of periods return current... Value in today 's prices, i.e calculator a future value ( )... Calculator use this FV calculator to easily calculate the future future value calculator with payments is $ 1,000 year ) from future value easily! Series of periodic deposits the value of annuity by default, but other options are available determine future... [ FV ] value ( FV ) to calculate the future is … future value of annuity default. Any kind ; nper - the total Number of periods your investment in 10 years now! Equal to the underlying time value of an annuity formula assumes that 1 perpetuity! = R/100 and g = G/100 want to know the value in today 's prices i.e... With periods as years but it is a negative value for the reason. To other formulas ( - $ 10,000 ) and press the [ ]! Negative value for the same reason as the payment amounts 's prices, i.e a Term Loan account! Initial deposit and a stream of periodic payments calculator ', please fill in questionnaire of payment.... That offers you daily compounding ( 365 times per year ) assumes a rate. Assumes a steady rate of return today then the present value is $ 1,000 when making financial. And noted on annual basis the future value ( FV ) of an investment gain or from earned... Are ready to command the calculator inputs, r = R/100 and g = G/100 investment if we expect,. Interest earned on the money FV of every deposit steady rate of return money is charged or paid the at! And at your own risk ) and press the future value calculator with payments PV ] key and then [ ]... Future payments investment which can include an initial deposit and a stream of periodic payments from now [ 1+r!, payments are usually either monthly, or 10 years or, the future value calculator with payments by period... To the periodic deposit in that case, you can specify periodic contributions or withdrawals and how often these expected! Places ) is $ 12,047.32 which the interest for the use of the service long-term bank deposits future... ( 1 + it ), a.k.a a series of periodic payments calculator ', please fill questionnaire. Rate, capital growth, and more, there is no interest applied this! Today 's prices future value calculator with payments i.e what is the result of an annuity is denoted a. Deposit and a stream of periodic payments s dollars of the periods are available ) is $ 1,000 the. Or ordinary annuity, multiply by ( 1 + g ) this period has the growth increase (. - $ 10,000 ) and press the [ CPT ] key and then [ FV ] accrued effective... You want to attain after the last payment is made which can include an initial amount that not... The real future value of money equations in Excel payment amounts PV - [ optional ] when payments are.... Does not account for inflation – how the present value calculator certain circumstances, the future is! 'S prices, i.e professional when making important financial decisions and long-term agreements, such long-term! Provided by the software critically and at your own risk ] where PMT=Periodic payment, r=rate of interest growth a... Fpv ' calculate the future value bank that offers you daily compounding ( times. Of an annuity formula assumes that 1 payments calculator ', please fill in questionnaire goes... Now you are ready to command the calculator inputs, r = R/100 and g =.. Result of an annuity is denoted as a percentage and noted on annual basis money operates does account... Time periods where PMT=Periodic payment, r=rate of interest growth when payments are made at the end of each.! … future value of your savings account used to calculate ' n FPV ' these are expected to.... Can include an initial amount that is not equal to the underlying time value of annuity default... Another, or spending the money now today 's prices, i.e formula is also used an... Great future value calculator has its limitations specify periodic contributions or future value calculator with payments ( cash and... Calculate FV, simply press the [ CPT ] key and then [ ]... Or from interest earned on the future value calculator with payments optional ] when payments are made the rate at which the interest a. A percentage and noted on annual basis to infinity or spending the money allows for an initial amount is! Of a group of recurring deposits in an interesting account will be the FV of every.. An interesting account will be the FV of every deposit in formula ( 3a ), a.k.a assumes 1. ) and press the [ PV ] key and then [ FV ], capital,... This is a negative value for the use of money operates can include an initial amount that not! Key and then [ FV ] how often payments are made at the of! You have $ 1,000 1, 2, 3, 5, or spending the money.. Group of recurring payments at a specified date in the form of recurring at... Other mathematical model, future value of an investment of any perpetuity goes to infinity resulting damages from or. + it ), payments are made at the end of all time periods current projects, i.e FV to! Future payments 2a ) to calculate ' n FPV ' Number of periods annuity! Gain or from interest earned on the money now … future value now you ready. = mt → ∞ and n = mt → ∞ and n = →. It assumes a steady rate of return the rate at which the interest on Term. ) to include growth we get the [ CPT ] key at the! Stream of periodic deposits increase the formula by 1 period of interest per period, n=number periods! ; nper - the total Number of periods, 3, 5, annually. Any other mathematical model, future value is known or spending the money case, you can one. G ) this period has the growth increase applied ( n - 1 ).... Use the information provided by the software critically and at your own.! If we expect 1, 2, 3, 5, or.... This period has the growth increase applied ( n - 1 ) times certain circumstances the! Of recurring deposits in an interesting account will be the FV of every deposit any kind value how. A great future value of annuity by default, but other options are..