Calculate Future Value with Recurring Deposits
Using the following values: The formula for the future value of an annuity due is d*(((1 + i)^t - 1)/i)*(1 + i) See Calculating The Present And Future Value Of Annuities In an annuity due, a deposit is made at the beginning of a period and the interest is received at the end of the period.  This is in contrast to an ordinary  annuity, where a payment is made at the end of a period. The formula is derived, by induction , from the summation of the future values of every deposit.  The initial value, with interest accumulated for all periods, can simply be added. So the overall formula is Let's break this into two parts, the future value of the initial deposit, and the future value of the payments: D(1 + i)n For the future value of the payments A((1+i)n-1) / i) Adding those two formulas together will give you the amount of money that should be in your account at the end.  Remember to make the appropriate adjustments to interest rate and the number of payments.  Divide the interest rate by the number of periods in a year (four for quarterly, twelve for monthly), and multiply the number of periods (p) by the same number.  Of course the monthly deposit amount will need to be in the same terms. See also: Annuity (finance theory) - Wikipedia
O boy you can take an entire on this. Here are the basics. Project future cash flows on a series of underlying assumptions such as growth rate and risk free rate. You then have to adjust top line items such as depreciation and come up with FCF. Then discount everything back with a terminal value. "If it could, it seems yet to be proven.  Long Term Capital Management was founded by a bunch of math whizzes and they seem to have missed something.  I'd never suggest that something has no value, but similar to the concept that ""if time travel were possible, why hasn't anyone come back from the future to tell us"" I'd suggest that if there were a real advantage to what you suggest, someone would be making money from it already.  In my opinion, the math is simple, little more than a four function calculator is needed." One way I heard of, from a friend who ran a similar fund as yours, is to calculate $days of investment and divide the investment as accordingly.  For example, If I invested 10$ for 10 days and you have invested 20$ for 5 days. At the end of the 10th day my $day = 10*10=100, while your $day=20*5=100. If the investement has grown to 100$, the I should get $100/(100+100)*100=$50, you also should get the same. This I guess is equitable, you could try dividing the corpus with above method. It consideres the amount invested as well as the time invested for. I think by the above method, you could also handle the inbetween withdrawals. This calculation arrives at the correct answer.  However, it uses the formula for an annuity due.  This means the payments are made at the beginning of the month and the last month of the 10 year period has interest accrued. See the section, Calculating the Future Value of an Annuity Due. The rate is given as an effective rate. with  In Excel, =FV((1+0.12)^(1/12)-1,120,3500,0,1) "I got $3394.83 The first problem with this is that it is backwards.  The NPV (Net Present Value) of three future payments of $997 has to be less than the nominal value.  The nominal value is simple:  $2991.   First step, convert the 8% annual return from the stock market to a monthly return.  Everyone else assumed that the 8% is a monthly return, but that is clearly absurd.  The correct way to do this would be to solve for m in  But we often approximate this by dividing 8% by 12, which would be .67%.  Either way, you divide each payment by the number of months of compounding.   Sum those up using m equal to about .64% (I left the calculated value in memory and used that rather than the rounded value) and you get about $2952.92 which is smaller than $2991.   Obviously $2952.92 is much larger than $2495 and you should not do this.  If the three payments were $842.39 instead, then it would about break even.   Note that this neglects risk.  In a three month period, the stock market is as likely to fall short of an annualized 8% return as to beat it.  This would make more sense if your alternative was to pay off some of your mortgage immediately and take the payments or yp pay a lump sum now and increase future mortgage payments.  Then your return would be safer.   Someone noted in a comment that we would normally base the NPV on the interest rate of the payments.  That's for calculating the NPV to the one making the loan.  Here, we want to calculate the NPV for the borrower.  So the question is what the borrower would do with the money if making payments and not the lump sum.   The question assumes that the borrower would invest in the stock market, which is a risky option and not normally advisable.  I suggest a mortgage based alternative.  If the borrower is going to stuff the money under the mattress until needed, then the answer is simple.  The nominal value of $2991 is also the NPV, as mattresses don't pay interest.  Similarly, many banks don't pay interest on checking these days.  So for someone facing a real decision like this, I'd almost always recommend paying the lump sum and getting it over with.  Even if the payments are ""same as cash"" with no premium charged." "Option pricing models used by exchanges to calculate settlement prices (premiums) use a volatility measure usually describes as the current actual volatility.  This is a historic volatility measure based on standard deviation across a given time period - usually 30 to 90 days.   During a trading session, an investor can use the readily available information for a given option to infer the ""implied volatility"".  Presumably you know the option pricing model (Black-Scholes).  It is easy to calculate the other variables used in the pricing model - the time value, the strike price, the spot price, the ""risk free"" interest rate, and anything else I may have forgotten right now.  Plug all of these into the model and solve for volatility.  This give the ""implied volatility"", so named because it has been inferred from the current price (bid or offer). Of course, there is no guarantee that the calculated (implied) volatility will match the volatility used by the exchange in their calculation of fair price at settlement on the day (or on the previous day's settlement).  Comparing the implied volatility from the previous day's settlement price to the implied volatility of the current price (bid or offer) may give you some measure of the fairness of the quoted price (if there is no perceived change in future volatility).  What such a comparison will do is to give you a measure of the degree to which the current market's perception of future volatility has changed over the course of the trading day.   So, specific to your question, you do not want to use an annualised measure.  The best you can do is compare the implied volatility in the current price to the implied volatility of the previous day's settlement price while at the same time making a subjective judgement about how you see volatility changing in the future and how this has been reflected in the current price." Okay, I think I managed to find the precise answer to this problem! It involves solving a non-linear exponential equation, but I also found a good approximate solution using the truncated Taylor series. See below for a spreadsheet you can use. Let's start by defining the growth factors per period, for money in the bank and money invested:   Now, let S be the amount ready to be invested after n+1 periods; so the first of that money has earned interest for n periods. That is,  The key step to solve the problem was to fix the total number of periods considered. So let's introduce a new variable: t = the total number of time periods elapsed So if money is ready to invest every n+1 periods, there will be t/(n+1) separate investments, and the future value of the investments will be:  This formula is exact in the case of integer t and n, and a good approximation when t and n are not integers. Substituting S, we get the version of the formula which explicitly depends on n:  Fortunately, only a couple of terms in FV depend on n, so we can find the derivative after some effort:  Equating the derivative to zero, we can remove the denominator, and assuming t is greater than zero, we can divide by the constant ( 1-G t ):  To simplify the equation, we can define some extra constants:    Then, we can define a function f(n) and write the equation as:  Note that α, β, γ, G, and R are all constant. From here there are two options: Use Newton's method or another numerical method for finding the positive root of f(n). This can be done in a number of software packages like MATLAB, Octave, etc, or by using a graphics calculator. Solve approximately using a truncated Taylor series polynomial. I will use this method here. The Taylor series of f(n), centred around n=0, is:  Truncating the series to the first three terms, we get a quadratic polynomial (with constant coefficients):  Using R, G, α, β and γ defined above, let c0, c1 and c2 be the coefficients of the truncated Taylor series for f(n):    Then,  n should be rounded to the nearest whole number. To be certain, check the values above and below n using the formula for FV. Using the example from the question: For example, I might put aside $100 every week to invest into a stock   with an expected growth of 9% p.a., but brokerage fees are $10/trade.   For how many weeks should I accumulate the $100 before investing, if I   can put it in my high-interest bank account at 4% p.a. until then? Using Newton's method to find roots of f(n) above, we get n = 14.004. Using the closed-form approximate solution, we get n = 14.082. Checking this against the FV with t = 1680 (evenly divisible by each n + 1 tested): Therefore, you should wait for n = 14 periods, keeping that money in the bank, investing it together with the money in the next period (so you will make an investment every 14 + 1 = 15 weeks.) Here's one way to implement the above solution with a spreadsheet. StackExchange doesn't allow tables in their syntax at this time, so I'll show a screenshot of the formulae and columns you can copy and paste: Formulae:  Copy and paste column A: Copy and paste column B: Results:  Remember, n is the number of periods to accumulate money in the bank. So you will want to invest every n+1 weeks; in this case, every 15 weeks. This investment does not have a payback period as the net present value of your investment is negative. Your investment requires an initial cash outlay of $40,000 followed by annual savings of $2060 for the next 20 years. Your discount rate is 5% at which the NPV is $-14327.85 as calculated below by using this JavaScript financial functions library tadJS that is based on a popular tadXL add-in for Excel 2007, 2010 and 2013. Recurring deposit means you put aside a sum every month to go into your RD account. Fixed deposit means you put aside a lump sum to go into your FD account. If we take investing 12,000 for RD, means 1,000 a month, and 12,000 for FD, means putting in 12,000 straightaway, we will definitely earn more from FD. However, if you do not have a lot of capital at the start, an RD is a good way to start saving in a disciplined manner. When calculating the NPV, is there anything I need to do in between the project start date outlay (Nov 2017), and the first cash inflow (July 2019). Do I need to discount the cashflow to the present, and if so, how? Yes, you need to discount every cash flow to the present time, not just the first one.   When discounting cash flows, the appropriate discount rate needs to represent the opportunity cost of the initial cash outlay.  Meaning if you were to use that money for something else, what rate of return would you expect? You could be safe and assume only a risk-free return (like 2-3%) or use the average rate of return of other investments (e.g. 10-15%). Another common approach is to use your cost of capital if you're raising funds for the project, or would instead have use the funds to pay off existing debt. Once you find a relevant discount rate, then just discount each cash flow by dividing them by e^rt, where r is the annualized discount rate (e.g. 0.10 for 10%) and t is the decimal number of years between now and the cash flow (e.g. 1.5 for 18 months) &gt; 1)What is the formula to turn the annualized rate into a monthly rate?  What do you *think* it is?   &gt; 2)What is the formula to find out the NPV of monthly cash flows?  Same one as usual. Remember, value can only be summed if it's *at the same point in time.*   &gt; For example, if I get $1000, $2000, and $3000 in months 1, 2, and 3, how do I calculate how much each of those are equal to as a present value if the annual discount rate is 8%?  Think it through. "To calculate the balance (not just principal) remaining, type into your favorite spreadsheet program: It is important that the periods for ""Periods"" and ""Rate"" match up.  If you use your annual rate with quarterly periods, you will get a horribly wrong answer. So, if you invest $1000 today, expect 6% interest per year (0.5% interest per month), withdraw $10 at the end of each month, and want to know what your investment balance will be 2 years (24 months) from now, you would type: And you would get a result of $872.84. Or, to compute it manually, use the formula found here by poster uart:   This is often taught in high-school here as a application of geomentric series. The derivation goes like this.  Using the notation :  r = 1 + interest_rate_per_term_as_decimal p = present value a = payment per term eot1 denotes the FV at end of term 1 etc.  eot1: rp + a   eot2: r(rp + a) + a = r^2p + ra + a   eot3: r(r^2p + ra + a) + a = r^3p + r^2a + ra + a ...   eotn: r^np + (r^(n-1) + r^(n-2) + ... 1)a = p r^n + a (r^n - 1)/(r-1)  That is, FV = p r^n + a (r^n - 1)/(r-1).   This is precisely what exel [sic] computes for the case of payments made at the end of each term (payment type = 0). It's easy enough to repeat the calculations as above for the case of payments made at the beginning of each term. This won't work for changing interest rates or changing withdrawal amounts.  For something like that, it would be better for you (if you don't want online calculators) to set up a table in a spreadsheet so you can adjust different periods manually." This is a present value calculation, which excel or any financial calculator can handle.  N = 300 (months) %i = 5/12 or .05/12 depending on the program/calculator PMT = $5000 (the monthly payment) FV = 0 (you want to end at zero balance) This calculates a PV (present value of $855,300)  Chad had it right, but used a calculator that didn't offer the PV function, so he guessed and changed numbers til the answer was clear. user379 makes a good point, but why start inflation calculations at 65, and not now? You look like you're in your 30's, so there's 30 years of inflation, and $60K/yr in today's value will need to be closer to $150K/yr, given about 30 years of 3% inflation. Im creating a 5-year projection on Profit and loss, cash flow and balance sheet and i\m suppose to use the LIBOR (5 year forward curve) as interest rate on debt.  This is the information i am given and it in USD.  Thanks for the link.  I guess its the USD LIBOR today, in one year, in two years, three years, four years and five years If you didn't have deposits, then the growth rate is simply ((p1/p0)^(1/t))-1, where p0 is the initial balance, p1 is the current balance, and t is the number of periods. For example, suppose you started the account with $100,000 in 2000. It's now 2015 -- 15 years later -- and the balance is $240,000. So the growth is: If you're making regular deposits, especially if you're making deposits of unequal amounts, the problem becomes much more complex. The easiest thing to do is probably to create a spreadsheet. Make a column for principle, a column for deposit amount, and a column for percent growth that period. Assuming A is principle and B is deposit, then the formula for growth C is =((A2-A1-B1)/A1-1)*100. Copy this formula down the column and Excel should automatically adjust the row numbers. Assuming you put one row for each month you can see the growth (or loss) month by month. You can get a general idea of what your overall growth rate has been by taking the average of the monthly amounts, but this would not be a truly accurate measure of your total growth because presumably (hopefully) you have more money in the later months than the earlier months. But it would be a good measure of how your investments are doing.