How to calculate years until financial independence?
"The definition I use for financial independence is 99% confidence that, at a specific estimated spending rate per year (allowing for estimated inflation, and budgeting for likely medical emergencies, and taxes on taxable investments), the money will outlast me. This translates to needing an average annual return on investment which covers the average yearly spending. For my purposes, that works out to my relying on being able to draw only a 4% income from the money each year, which should give me good odds of the money not just being sufficient but being able to deliver that rate ""forever"". (Historically, average US stock market rate if return is around 8%.) That is overkill, if course, I could plan on the money just barely lasting past my 120th birthday or something of that sort, but the goal us to be pretty sure not only that I won't run out but that I will have some cash unexpected needs. Which in turn means that I estimate I need investments 1/.04 times the yearly spending estimate to declare the ""forever"" independence/retirement, or 25x the yearly. From that, I can calculate how much longer, at a given savings rate and rate of return, it'll take for me to reach that target.  Obviously you need to adjust all these numbers to reflect your opinions/understanding if the market, your own needs, your priorities and expected maximum age, and the phase of Saturn's moons. But that's the basic rationale. Or you can pay a financial planner to give you this number, and a strategy for getting there, based on the numbers you give him or her plus some statistical analysis of the market's overall history." In this equation the withdrawal rate is the percent you must pull from your savings to meet your expenses. For example if your savings is $100,000 and you need $10,000 annually for your living expenses then your withdrawal rate would be 10% (where 10k is 10% of 100k).  To complete this formula, you need to know how much savings you need to be financially independent before you can use this formula to find out how long it will take you.
"The best way to do this is to use IRR.  It's a complicated calculation, but will take into account multiple in/out cash flows over time along with ""idle periods"" where your money may not have been doing anything.  Excel can calculate it for you using the XIRR function" It's important to have both long term goals and milestones along the way. In an article I wrote about saving 15% of one's income, I offered the following table:  This table shows savings starting at age 20 (young, I know, so shift 2 years out) and ending at 60 with 18-1/2 year's of income saved due to investment returns. The 18-1/2 results in 74% of one's income replaced at retirement if we follow the 4% rule. One can adjust this number, assuming Social Security will replace 30%, and that spending will go down in retirement, you might need to save less than this shows. What's important is that as a starting point, it shows 2X income saved by age 30. Perhaps 1X is more reasonable. You are at just over .5X and proposing to spend nearly half of that on a single purchase.  Financial independence means to somehow create an income you can live on without the need to work. There are many ways to do it, but it usually starts with a high saving rate. Your numbers suggest a good income now, but maybe this is only recently, else you'd have over $200K in the bank.  I suggest you read all you can about investments and the types of retirement accounts, including 401(k) (if you have that available to you), IRA, and Roth IRA. The details you offer don't allow me to get much more specific than this. "To buy a house, you need: At least 2 years tax returns (shows a steady income history; even if you're making 50k right now, you probably weren't when you were 16, and you might not be when you're 20; as they say, easy come, easy go). A 20% down payment.  These days, that easily means writing a $50k check.  You make $50k a year, great, but try this math: how long will it take you to save 100% of your annual salary?  If you're saving 15% of your income (which puts you above many Americans), it'll still take 7 years.  So no house for you for 7 years. While your attitude of ""I've got the money, so why not"" is certainly acceptable, the reality is that you don't have a lot of financial experience yet.  There could easily be lean times ahead when you aren't making much (many people since 2008 have gone 18 months or more without any income at all). Save as much money as possible.  Once you get $10k in a liquid savings account, speak to a CPA or an investment advisor at your local bank to set up tax deferred accounts such as an IRA.  And don't wait to start investing; starting now versus waiting until you're 25 could mean a 100% difference in your net worth at any given time (that's not just a random number, either; an additional 7 years compounding time could literally mean another doubling of your worth)." I recommend pulling up a retirement calculator and having an honest conversation about how long term savings works, and the power of compound interest. Just by playing around with the sliders on an online calculator, you can demonstrate how the early years are the most important. Depending on how much they make now and are considering saving, delaying 5-10 years can easily leave 6-7 figures on the table. If it's specifically a child or close family member, I recommend pulling up your retirement account. Talk with them about how you managed it, and how much you were putting in. Perhaps show them how much is the principal and how much is interest. If you did well, tell them how. If you didn't do as well as you liked, tell them what you would have done differently. Finally, discuss a bit of psychology. Even if they don't have a professional job and are making minimum wage, getting into the habit of saving makes it easier when they eventually make more. A couple of dollars a month isn't much, but getting into the habit makes it easier to save a couple hundred dollars a month later on. "Wow, this turns out to be a much more difficult problem than I thought from first looking at it. Let's recast some of the variables to simplify the equations a bit. Let rb be the growth rate of money in your bank for one period. By ""growth rate"" I mean the amount you will have after one period. So if the interest rate is 3% per year paid monthly, then the interest for one month is 3/12 of 1% = .25%, so after one month you have 1.0025 times as much money as you started with. Similarly, let si be the growth rate of the investment. Then after you make a deposit the amount you have in the bank is pb = s. After another deposit you've collected interest on the first, so you have pb = s * rb + s. That is, the first deposit with one period's growth plus the second deposit. One more deposit and you have pb = ((s * rb) + s) * rb + s = s + s * rb + s * rb^2. Etc. So after n deposits you have pb = s + s * rb + s * rb^2 + s * rb^3 + ... + s * rb^(n-1). This simplifies to pb = s * (rb^n - 1)/(rb - 1). Similarly for the amount you would get by depositing to the investment, let's call that pi, except you must also subtract the amount of the broker fee, b. So you want to make deposits when pb>pi, or s*(ri^n-1)/(ri-1) - b > s*(rb^n-1)/(rb-1) Then just solve for n and you're done! Except ... maybe someone who's better at algebra than me could solve that for n, but I don't see how to do it. Further complicating this is that banks normally pay interest monthly, while stocks go up or down every day. If a calculation said to withdraw after 3.9 months, it might really be better to wait for 4.0 months to collect one additional month's interest. But let's see if we can approximate. If the growth rates and the number of periods are relatively small, the compounding of growth should also be relatively small. So an approximate solution would be when the difference between the interest rates, times the amount of each deposit, summed over the number of deposits, is greater than the fee. That is, say the investment pays 10% per month more than your bank account (wildly optimistic but just for example), the broker fee is $10, and the amount of each deposit is $200. Then if you delay making the investment by one month you're losing  10% of $200 = $20. This is more than the broker fee, so you should invest immediately. Okay, suppose more realistically that the investment pays 1% more per month than the bank account. Then the first month you're losing 1% of $200 = $2. The second month you have $400 in the bank, so you're losing $4, total loss for two months = $6. The third month you have $600 in the bank so you lose an additional $6, total loss = $12. Etc. So you should transfer the money to the investment about the third month. Compounding would mean that losses on transferring to the investment are a little higher than this, so you'd want to bias to transferring a little earlier. Or, you could set up a spreadsheet to do the compounding calculations month by month, and then just look down the column for when the investment total minus the bank total is greater than the broker fee. Sorry I'm not giving you a definitive answer, but maybe this helps." According to my reading, the Trinity study says you can withdraw 4% a year for 30 years without exhausting your nest egg, not necessarily that it won't shrink. In most cases, your nest egg will indeed grow. But unfortunately you can't plan to leave no estate while simultaneously preparing for worst-case scenarios in case you happen to pick a bad year to stop working. You can run simulations based on historical data on sites like cFIREsim. And once you're retired, you could potentially increase your spending if simulations show that you're likely to leave behind a large estate. You also probably want to look into things like charitable remainder trusts. The CFA will generally take 3-4 years to finish. They test level 2 and 3 once a year and level 1 twice. They recommend approx 300 hours of studying for each level, but you can get away with less. But for you, level 1 is going to be your undergrad in finance so it shouldn’t be anything outside of your normal course of study. You’ll be able to save time on studying if you take it while the material is still fresh "Time Value of Money - The simple calculation for this is FV = PV * (1+r)^N which reads The Future Value is equal to the Present Value times 1 plus the interest rate multiplied by itself by the number of periods that will pass. A simple way to look at this is that if interest rates were 5%/yr a dollar would be worth (1.05)^N where N is the number of years passing.  The concept of compound interest cannot be separated from the above. Compounding is accounting for the interest on the interest that has accrued in prior periods. If I lend you a dollar at 6% simple interest for 30 years, you would pay me back $1 + $1.80 or $2.80. But - 1.06^30 = 5.74 so that dollar compounded at 6% annually for 30 years is $5.74. Quite a difference.  Often, the time value of money is discussed in light of inflation. A dollar today is not the same dollar as 30 years ago or 30 years hence. In fact, inflation has eroded the value of the dollar by a factor of 3 over the past 30 years. An average item costing $100 would now cost $300. So when one invests, at the very least they try to stay ahead of inflation and seek additional return for their risk.  One quirk of compounding is the ""rule of 72."" This rule states that if you divide the interest rate into the number 72 the result is the number of years to double. So 10% per year will take about 7.2 years to double, 8%, 9 years, etc. It's not 100% precise, but a good ""back of napkin"" calculation.  When people talk about the total payments over the thirty year life of a mortgage, they often ignore the time value of money. That payment even ten years from now has far less value than the same payment today." You can't get there from here.  This isn't the right data.  Consider the following five-year history:  2%, 16%, 32%, 14%, 1%.  That would give a 13% average annual return.  Now compare to -37%, 26%, 15%, 2%, 16%.  That would give a 4% average annual return.   Notice anything about those numbers?  Two of them are in both series.  This isn't an accident.  The first set of five numbers are actual stock market returns from the last five years while the latter five start three years earlier.  The critical thing is that five years of returns aren't enough.  You'd need to know not just how you can handle a bull market but how you do in a bear market as well.  Because there will be bear markets.   Also consider whether average annual returns are what you want.  Consider what actually happens in the second set of numbers:   But if you had had a steady 4% return, you would have had a total return of 21%, not the 8% that would have really happened.  The point being that calculating from averages gives misleading results.  This gets even worse if you remove money from your principal for living expenses every year.   The usual way to compensate for that is to do a 70% stock/30% bond mix (or 75%/25%) with five years of expenses in cash-equivalent savings.  With cash-equivalents, you won't even keep up with inflation.  The stock/bond mix might give you a 7% return after inflation.  So the five years of expenses are more and more problematic as your nest egg shrinks.  It's better to live off the interest if you can.  You don't know how long you'll live or how the market will do.   From there, it's just about how much risk you want to take.  A current nest egg of twenty times expenses might be enough, but thirty times would be better.  Since the 1970s, the stock market hasn't had a long bad patch relative to inflation.  Maybe you could squeak through with ten.  But if the 2020s are like the 1970s, you'd be in trouble. These are the steps I'd follow: $200 today times (1.04)^10 = Cost in year 10.  The 6 deposits of $20 will be one time value calculation with a resulting year 7 final value. You then must apply 10% for 3 years (1.1)^3 to get the 10th year result.  You now have the shortfall. Divide that by the same (1.1)^3 to shift the present value to start of year 7. (this step might confuse you?) You are left with a problem needing 3 same deposits, a known rate, and desired FV. Solve from there.  (Also, welcome from quant.SE. This site doesn't support LATEX, so I edited the image above.) "Another approach would be more personalized, which is to measure the risk of missing your goals, rather than measuring the risk of an investment in some abstract sense. Financial planners do this for example with Monte Carlo simulation software (see http://en.wikipedia.org/wiki/Monte_Carlo_method). They would put in a goal such as not running out of money before you die, with assumptions such as the longest you might live and how much you'll withdraw every year. You'd also assume an asset allocation. The Monte Carlo simulation then generates random market movements over the time period, considering historical behavior of your asset allocation, and each run of the simulation would either succeed (you are able to support yourself until death) or fail (you run out of money). The risk measure is the percentage of simulation runs that fail. You can do this to plan saving for retirement in addition to planning withdrawals; then your goal would be to have X amount of money in real after-inflation dollars, perhaps, and success is if you end up with it, and failure is if you don't. The great thing about this risk measure is that it's relevant and personal; ""10% chance of being impoverished at age 85,"" ""20% chance of having to work an extra decade because you don't have enough at 65,"" these kinds of answers. Which is a lot easier to act on than ""the variance is 10"" or ""the beta is 1.5"" - would you rather know your plan has a 90% chance of success, or know that you have a variance of 10? Both numbers are probably just guesses, but at least the ""chance of success"" measure is actionable and relevant. Some tangential thoughts FWIW:" The rule that I know is six months of income, stored in readily accessible savings (e.g. a savings or money market account).   Others have argued that it should be six months of expenses, which is of course easier to achieve.  I would recommend against that, partially because it is easier to achieve.  The other issue is that people are more prone to underestimate their expenses than their income.  Finally, if you base it on your current expenses, then budget for savings and have money left over, you often increase your expenses.  Sometimes obviously (e.g. a new car) and sometimes not (e.g. more restaurants or clubs).  Income increases are rarer and easier to see.   Either way, you can make that six months shorter or longer.  Six months is both feasible and capable of handling difficult emergencies.  Six years wouldn't be feasible.  One month wouldn't get you through a major emergency.   Examples of emergencies:   Your savings can be in any of multiple forms.  For example, someone was talking about buying real estate and renting it.  That's a form of savings, but it can be difficult to do withdrawals.  Stocks and bonds are better, but what if your emergency happens when the market is down?  Part of how emergency funds operate is that they are readily accessible.   Another issue is that a main goal of savings is to cover retirement.  So people put them in tax privileged retirement accounts.  The downside of that is that the money is not then available for emergencies without paying penalties.  You get benefits from retirement accounts but that's in exchange for limitations.   It's much easier to spend money than to save it.  There are many options and the world makes it easy to do.  Emergency funds make people really think about that portion of savings.  And thinking about saving before spending helps avoid situations where you shortchange savings.   Let's pretend that retirement accounts don't exist (perhaps they don't in your country).  Your savings is some mix of stocks and bonds.  You have a mortgaged house.  You've budgeted enough into stocks and bonds to cover retirement.  Now you have a major emergency.   As I understand your proposal, you would then take that money out of the stocks and bonds for retirement.  But then you no longer have enough for retirement.  Going forward, you will have to scrimp to get back on track.   An emergency fund says that you should do that scrimping early.  Because if you're used to spending any level of money, cutting that is painful.  But if you've only ever spent a certain level, not increasing it is much easier.  The longer you delay optional expenses, the less important they seem.   Scrimping beforehand also helps avoid the situation where the emergency happens at the end of your career.  It's one thing to scrimp for fifteen years at fifty.  What's your plan if you would have an emergency at sixty-five?  Or later?  Then you're reducing your living standard at retirement.   Now, maybe you save more than necessary.  It's not unknown.  But it's not typical either.  It is far more common to encounter someone who isn't saving enough than too much. I would use neither method.  Taking a short example first, with just three compounding periods, with interest rate 10%.  The start value y0 is 1. So after three years the value is 1.331, the same as y0 (1 + 0.1)^3. Depreciating (like inflation) by 10% (to demonstrate) gets us back to y0 = 1 Appreciating and depreciating by 10% cancels out: Appreciating by 10% interest and depreciating by 3% inflation: This is the same as y0 (1 + 0.1)^3 (1 + 0.03)^-3 = 1.21805 So for 50 years the result is y0 (1 + 0.1)^50 (1 + 0.03)^-50 = 26.7777 Note You can of course use subtraction but the not using the inflation figure directly.  E.g. (edit: This appears to be the Fisher equation.) 2nd Note Further to comments, here is a chart to illustrate how much the relative performance improves when inflation is accounted for.  The first fund's return is 6% and the second fund's return varies from 3% to 6%.  Inflation is 3%. Congrats on saving aggressively when you're young. I'm not a huge fan of tax-advantaged accounts because the rules can change on them, and there's already a penalty for you to take out that money for most purposes until you've almost tripled your age. Free money (a match) overcomes this reservation for me, but I'm not contributing anything beyond that.  I'm paying my taxes on the rest and am done with them. Watching your money grow tax-free for another 37 1/2 years only to see your (and everyone else's) marginal tax rate rise isn't much fun.  I'm not saying that will happen, but it certainly could. "Some details in case you are interested: Being a defined benefit kind of pension plan, the formula for your Social Security benefits isn't tied directly to FICA contributions, and I'm not aware of any calculator that performs an ROI based on FICA contributions. Rather, how much you'll get in retirement is based on your average indexed monthly earnings.  Here's some information on the Social Security calculation from the Social Security Administration - Primary Insurance Amount (PIA): For an individual who first becomes eligible for old-age insurance   benefits or disability insurance benefits in 2013, or who dies in 2013   before becoming eligible for benefits, his/her PIA will be the sum of:       (a) 90 percent of the first $791 of his/her average indexed monthly earnings, plus       (b) 32 percent of his/her average indexed monthly earnings over $791 and through $4,768, plus       (c) 15 percent of his/her average indexed monthly earnings over $4,768. Here's an example.  Of course, to calculate a benefit in the future, you'll need to calculate projected average indexed monthly earnings; more details here.  You'll also need to make assumptions about what those bend points might be in the future.  The average wage indexing values for calculating the AIME are available from the Social Security Administration's site, but future indexing values will also need to be projected based on an assumption about their inflation.  You'll also need to project the Contribution and Benefit Base which limits the earnings used to calculate contributions and benefits. Also, the PIA calculation assumes benefits are taken at the normal retirement age.  Calculating an early or late retirement factor is required to adjust benefits for another age.  Then, whatever benefits you get will increase each year, because the benefit is increased based on annual changes in the cost of living. Performing the series of calculations by hand isn't my idea of fun, but implementing it as a spreadsheet (or a web page) and adding in some ""ROI based on FICA contributions"" calculations might be an interesting exercise if you are so inclined? For completeness sake, I'll mention that the SSA also provides source code for a Social Security Benefit Calculator."