Calculate time to reach investment goals given starting balance?
The Finance functions in spreadsheet software will calculate this for you.  The basic functions are for Rate, Payment, PV (present value), FV (Future value), and NPER, the number of periods.  The single calculation faces a couple issues, dealing with inflation, and with a changing deposit. If you plan to save for 30 years, and today are saving $500/mo, for example, in ten years I hope the deposits have risen as well. I suggest you use a spreadsheet, a full sheet, to let you adjust for this.  Last, there's a strange effect that happens. Precision without accuracy. See the results for 30-40 years of compounding today's deposit given a return of 6%, 7%, up to 10% or so. Your forecast will be as weak as the variable with the greatest range. And there's more than one, return, inflation, percent you'll increase deposits, all unknown, and really unknowable.  The best advice I can offer is to save till it hurts, plan for the return to be at the lower end of the range, and every so often, re-evaluate where you stand. Better to turn 40, and see you are on track to retire early, than to plan on too high a return, and at 60 realize you missed it, badly.  As far as the spreadsheet goes, this is for the Google Sheets -  Type this into a cell =nper(0.01,-100,0,1000,0) It represents 1% interest per month, a payment (deposit) of $100, a starting value of $0, a goal of $1000, and interest added at month end. For whatever reason, a starting balance must be entered as a negative number, for example - =nper(0.01,-100,-500,1000,0) Will return 4.675, the number of months to get you from $500 to $1000 with a $100/mo deposit and 1%/mo return. Someone smarter than I (Chris Degnen comes to mind) can explain why the starting balance needs to be entered this way. But it does show the correct result. As confirmed by my TI BA-35 financial calculator, which doesn't need $500 to be negative. "Here's a formula;  I had to go over to SEMath, use their MathJax to compose the answer and then paste this screen shot. As a result, I can't fix a typo:  ""ST"" is the same as ""St""" Fairly straightforward to match the result from the calculator soup link.  There is a formula to calculate n from the future value s (using natural logs) In Excel This was derived as shown  To calculate n from the inflation-adjusted future value si requires using a solver since an algebraic formula cannot be formulated.  As demonstrated  Calculations done using Mathematica 7.
Yes, assuming that your cash flow is constantly of size 5 and initial investment is 100, the following applies: IRR of 5% over 3 years: Value of CashFlows: 4.7619 + 4.5351 + 4.3192 = 13.6162 NPV: 100 - 13.6162 = 86.3838 Continuous compounding: 86.3838 * (1.05^3) = 100 "When using Time Value of Money equations, you need to know when the flow starts. A mortgage for example, has a first payment at the end of the first time period, usually 1 month.  For savings, one can start the account with a deposit of course, or start by saying ""I will deposit $XXX at the end of each month.  The answer really depends on the exact details of the situation. In your example, I'm inclined to suggest first flow is 1 year out." "The raw question is as follows:  ""You will be recommending a purposed portfolio to an investment committee (my class). The committee runs a foundation that has an asset base of $4,000,000. The foundations' dual mandates are to (a) preserve capital and (b) to fund $200,000 worth of scholarships. The foundation has a third objective, which is to grow its asset base over time.""   The rest of the assignment lays out the format and headings for the sections of the presentation.  Thanks, by the way - it's an 8 week accelerated course and I've been out sick for two weeks. I've been trying to teach myself this stuff, including the excel calculations for the past few weeks." There are at least a couple of ways you could view this to my mind: Make an Excel spreadsheet and use the IRR function to compute the rate of return you are having based on money being added. Re-invested distributions in a mutual fund aren't really an additional investment as the Net Asset Value of the fund will drop by the amount of the distribution aside from market fluctuation. This is presuming you want a raw percentage that could be tricky to compare to other funds without doing more than a bit of work in a way. Look at what is the fund's returns compared to both the category and the index it is tracking. The tracking error is likely worth noting as some index funds could lag the index by a sizable margin and thus may not be that great. At the same time there may exist cases where an index fund isn't quite measuring up that well. The Small-Growth Indexing Anomaly would be the William Bernstein article from 2001 that has some facts and figures for this that may be useful. Using a simple investment calculator to get a sense of scale here, to have 70k total, including the 500 a month invested, after ten years you just need returns of 2%.  To earn 70k on top of the money invested you would need returns over 20%.  To do that in five years you would need over 50% annual return. That is quite a big difference.  Annualized returns of 20% would require high risk and a very large amount of time invested, skill and luck.  2% returns can be nearly guaranteed without much effort. I would encourage you to think about your money more holistically. If you get very unlucky with investments and don't make any money will you not go on the vacations even if your income allows?  That doesn't make a lot of sense.  As always, spend all your money with the current and future in mind.  Investment return Euros are no different from any other Euros. At that point, the advice is the same for all investors try to get as much return as possible for the risk you are comfortable with.  You seem to have a high tolerance for risk.  Generally, for investors with a high risk tolerance a broadly diversified portfolio of stocks (with maybe a small amount of bonds, other investments) will give the most return over the long term for the risk taken. After that generally the next most useful way to boost your returns is to try to avoid taxes which is why we talk about 401(k)s so much around here.  Each European country has different tax law, but please ask questions here about your own country as well as you mention money.se could use more ex-US questions. Retirement calculation, in general, should be based on the amount of money needed per year/month and the expected life expectancy. Life expectancy, if calculated to 90 years (let's say) indicates that post retirement age (60 yrs.) your accumulated/invested money should generate adequate income to cover your expenses till 90 years. The problem in general is not how long you shall live but what would be your expected spending from retirement to end of life expectancy. The idea is at the minimum your investments should generate income that is inflation adjusted. One way to do this is to consider your monthly expense now i.e. the expense that is absolute minimum for carrying on (food, electricity, water, medicines, household consumables, car petrol, insurance, servicing, entertainment, newspaper etc.) this does not contain the amortizable liabilities (home loan, child's education, other debts). It is better to take this amount per family rather than per person and yearly rather than monthly (as we tend to miss a lot of yearly expenses). This amount that you need today will increase at a Compounded Annual Growth Rate (CAGR) of the average inflation. For example, if today you spend 100 per year in 7 years you will need to spend appx. 200 at 10% inflation. Now, your investments will not increase post your retirement, so your current investment needs to do two things (1) give you your yearly requirement (2) grow by a fixed amount so that next year it can give you CAGR adjusted returns. In general, this kind of investment grows by high net amounts initially and slowly the growth decrease. The above can be calculated by Net Present value (NPV) formulae (http://en.wikipedia.org/wiki/Net_present_value). The key is to remember that the money that is invested when you retire should be able to give you inflation adjusted returns to cover your yearly expenses. How much money you need depends on your life style/expectation and how much return is received depends on the instruments that you invest on. As for your question above on the difference between the age of you and your spouse, it better to go with the consolidated family requirement and get an idea of how much investment is necessary and provision the same as soon as possible from your as well as your spouse's income. Hope this helps.- thanks Basically you'd take all the companies in a given universe (like the S&amp;P 500 or the Russell 3000) and instead of weighting them by market cap as they are currently done, you would weight by an alternative measure.  Right now, if you're invested in an index that is market cap weighted, you're effectively momentum chasing. If a stock runs up, you're going to have a higher weight in your portfolio because of it (but only after the increase).  An alternative that OppenheimerFunds has come up with is using revenue-weighting. That way you're using company fundamentals and only when the fundamentals are improving do you increase the weight in your portfolio.  I haven't yet seen any research that explores weighting by other fundamentals. I would think that revenues aren't perfect either and that you might want to weight by Net Income. Or to go several steps further, by year over year Free Cash Flow growth.   It could be a seminal paper if you are the one who empirically identifies a better weighting methodology and then have everyone else fight over the theoretical underpinnings.  This is effectively what goes into Smart Beta investing: http://www.investopedia.com/terms/s/smart-beta.asp 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) A couple ideas: Use excel - it has an IRR (internal rate of return) that can handle a table of inputs as you describe, along with dates deposited to give you a precise number.  Go simple - track total deposits over the year, assume half of that was present in January. So, for example, your account started the year with $10k, ended with $15k, but you deposited $4k over the year. It should be clear the return (gain) is $1k, right? But it's not 10%, as you added during the year. I'd divide $1k/$12k for an 8.3% return. Not knowing how your deposits were structured, the true number lies between the 10% and 6.7% as extremes. You'll find as you get older and have a higher balance, this fast method gaining accuracy, as your deposits are a tinier fraction of your account and likely spread out pretty smoothly over the year anyway. The author is using the simple Dietz method, (alternatively the modified Dietz), with the assumption that the net cash-flow occurs halfway through the time period.  Let's say the time period is one year for illustration, so the cash-flow would be at the end of the second quarter. The money-weighted method gives a more accurate return, but has to be solved by trial-and-error or using a computer.  The money-weighted return is 11.2718 % and the simple or modified Dietz return is 11.2676 %.  When the sums are done backwards to check, the Dietz is half a dollar out with a final value of $11,999.50 while the money-weighted return recalculates exactly $12,000. It is worth pointing out that the return changes if the cash-flow is not in the middle of the time period.  A case with the cash-flow at the end of Q3 is added to illustrate. The number you are trying to calculate is called the Internal Rate of Return (IRR).  Google Spreadsheets (and excel) both have an XIRR function that can do this for you fairly simply. Setup a spreadsheet with 1 column for dates, 1 column for investment. Mark your investments as negative numbers (payment to invest).  All investments will be negative. Mark your last row with today's date and today's valuation (positive). All withdrawals will be positive, so you are pretending to withdrawal your entire account for the purpose of calculation. Do not record dividends or other interim returns unless you are actually withdrawing money. The XIRR function will calculate your internal rate of return with irregularly timed investments. Links: Article explaining XIRR function (sample spreadsheet in google docs to modify) **Using your Time Value of Money functions on your calculator**   N = 3x2 = 6   PV = -914   PMT = (.16 x 1000)/2 = 80   FV = 1000    Compute I/Y  Or     **Step by step calculations**   1) Compute the PV of **(FV of Bond)**1000 in **(3x2)**6 periods at **(16%/2)**8% with no payments   2) Compute the PV of an Annuity of **(.16/2x1000)**$80 payments over **(3x2)**6 periods with an interest rate of **(16%/2)**8% and 0 Future Value   3) Combine the values from Steps 1 and 2 I would read any and all of the John Bogle books.  Essentially:  We know the market will rise and fall.  We just don't know when specifically.   For the most part it is impossible to time the market. He would advocate an asset allocation approach to investing.  So much to bonds, tbills, S&P500 index, NASDAQ index.  In your case you could start out with 10% of your portfolio each in S&P500 and NASDAQ.  Had you done that, you would have achieved growth of 17% and 27% respectively.  The growth on either one of those funds would have probably dwarfed the growth on the entire rest of your portfolio.  BTW 2013 and 2014 were also very good years, with 2015 being mostly flat. In the past you have avoided risk in the market to achieve the detrimental effects of inflation and stagnant money.  Don't make the same mistakes going forward. "Past results are not a predictor of future results. There is no explicit upper bound on a market, and even if individual companies' values were remaining unchanged one would expect the market to drift upward in the long term. Plus, there's been some  shift from managing companies for dividends to managing stocks for growth, which will tend to increase the upward push. Trying to time the market -- to guess when it's going to move in any particular direction -- is usually closer to gambling than investing. The simplest answer remains a combination of buy-and-hold and dollar-cost averaging. Buy at a constant number of dollars per month (or whatever frequency you prefer), and you will automatically buy more when the stock/fund is lower, less when it is higher. That takes advantage of downturns as buying opportunities without missing out on possible gains at the other end. Personally, I add a bit of contrarian buying to that -- I increased my buying another notch or two while the market was depressed, since I had money I wouldn't need any time soon (buy and hold) and I was reasonably confident that enough of the market would come back strongly enough that I wasn't at significant risk of losing the investment. That's one of the things which causes me to be categorized as an ""aggressive investor"" even though I'm operating with a very vanilla mix of mutual funds and not attempting to micromanage my money. My goal is to have the money work for me, not vice versa." "Treat each position or partial position as a separate LOT. Each time you open a position, a new lot of shares is created. If you sell the whole position, then the lot is closed. Done. But if you sell a partial quantity, you need to create a new lot. Split the original lot into two. The quantities in each are the amount sold, and the amount remaining. If you were to then buy a few more shares, create a third lot. If you then sell the entire position, you'll be closing out all the remaining lots. This allows you to track each buy/sell pairing. For each lot, simply calculate return based on cost and proceeds. You can't derive an annualized number for ALL the lots as a group, because there's no common timeframe that they share. If you wish to calculate your return over time on the whole series of trades, consider using TWIRR. It treats these positions, plus the cash they represent, as a whole portfolio. See my post in this thread: How can I calculate a ""running"" return using XIRR in a spreadsheet?"