How to calculate lump sum required to generate desired monthly income?
The product you seek is called a fixed immediate annuity.  You also want to be clear it's inflation adjusted. In the US, the standard fixed annuity for a 40year old male (this is the lowest age I find on the site I use) has a 4.6% return. $6000/ yr means one would pay about $130,000 for this. The cost to include the inflation adder is about 50%, from what I recall. So close to $200,000.  This is an insurance product, by the way, and you need to contact a local provider to get a better quote.
With 10% return over three years, depositing $900 each month, in three years $34,039.30.  Re. downvote. I guess this is too brief and without explanation, but I was rushing.  If you want further explanation of how this is calculated check the link already posted by JoeTaxpayer, and have a look at the formula for continuously compounded return.  Also, try out the numbers in the simplified example below yourself.  E.g.  Addendum mhoran_psprep has pointed out that I didn't read the OP's post closely enough.  With rolling investments the total return will be:  Where n is the month number i.e. 36, 37, etc. Not sure of your locality. In the USA, there are many options. There are many corporate bonds that pay interest monthly. You can invest in a handful of bonds, chosen so at least one of them pays interest each month. (Minimum investment requirements make this an expensive option)  Unit Trusts made of bonds (a handful of bonds wrapped into a single fixed investment) usually pay monthly interest. As the bonds begin to mature, the interest payments shrink (but you begin to get principal payments which can be reinvested). Bond mutual funds and ETFs usually provide monthly dividends (that come from the interest and capital gains of the bonds held by the fund). Dividends are usually consistent, but not necessarily fixed.  You can produce a monthly income from stocks in the same way as the above mentioned bond methods. Income can be consistent, but not fixed. If annualized rate of return is what you are looking for, using a tool would make it a lot easier.   In the post I've also explained how to use the spreadsheet.   Hope this helps. EDIT: After reading one of the comments on the original question, I realized that there is a much more intuitive way to think about this. If you look at it as a standard PV calculation and hold each of the cashflows constant. Really what's happening is that because of inflation the discount rate isn't the full value of the interest rate. Really the discount rate is only the portion of the interest rate above the inflation rate. Hence in the standard perpetuity PV equation PV = A / r r becomes the interest rate less the inflation rate which gives you PV = A / (i - g). That seems like a much better way to get to the answer than all the machinations I was originally trying. Original Answer: I think I finally figured this out. The general term for this type of system in which the payments increase over time is a gradient series annuity. In this specific example since the payment is increasing by a percentage each period (not a constant rate) this would be considered a geometric gradient series. According to this link the formula for the present value of a geometric gradient series of payments is: Where P is the present value of this series of cashflows.   A_1 is the initial payment for period 1 (i.e. the amount you want to withdraw adjusted for inflation).   g is the gradient or growth rate of the periodic payment (in this case this is the inflation rate)   i is the interest rate   n is the number of payments This is almost exactly what I was looking for in my original question. The only problem is this is for a fixed amount of time (i.e. n periods). In order to figure out the formula for a perpetuity we need to find the limit of the right side of this equation as the number of periods (n) approaches infinity. Luckily in this equation n is already well isolated to a single term: (1 + g)^n/(1 + i)^-n}. And since we know that the interest rate, i, has to be greater than the inflation rate, g, the limit of that factor is 0. So after replacing that term with 0 our equation simplifies to the following: Note: I don't do this stuff for a living and honestly don't have a fantastic finance IQ. It's been a while since I've done any calculus or even this much algebra so I may have made an error in the math. There are a number of scholarly articles on the subject including a number at the end of the Vanguard article you reference.  However, unfortunately like much of financial research you can't look at the articles without paying quite a bit. It is not easy to make a generic comparison between lump-sum and dollar cost averaging because there are many ways to do dollar cost averaging.  How long do you average over?  Do you evenly average or exponentially put the money to work?  The easiest way to think about this problem though is does the extra compounding from investing more of the money immediately outweigh the chance that you may have invested all the money when the market is overvalued.  Since the market is usually near the correct value investing in lump sum will usually win out as the Vanguard article suggests. As a side note, while using DCA on a large one time sum of money is generally not optimal, if you have a consistent salary DCA by frequently investing a portion of your salary has been frequently shown to be a very good idea of long periods over saving up a bunch of money and investing it all at once.  In this case you get the compounding advantage of investing early and you avoid investing a large chunk of money when the market is overvalued. The simplest way is just to compute how much money you'd have to have invested elsewhere to provide a comparable return. For example, if you assume a safe interest rate of 2.3% per year, you would need to have about $520,000 to get $1,000/month. Let P denote the amount of the investment, R the rate of return and I the rate of inflation.  For simplicity, assume that the payment p is made annually right after the return has been earned.  Thus, at the end if the year, the investment P has increased to P*(1+R) and p is returned as the annuity payment. If I = 0, the entire return can be paid out as the payment, and thus p = P*R. That is, at the end of the year, when the dust settles after the return P*R has been collected and paid out as the annuity payment, P is again available at the beginning of the next year to earn return at rate R. We have P*(1+R) - p = P If I > 0, then at the end of the year, after the dust settles, we cannot afford to have only P available as the investment for next year. Next year's payment must be p*(1+I) and so we need a larger investment since the rate of return is fixed.  How much larger?  Well, if the investment at the beginning of next year is P*(1+I), it will earn exactly enough additional money to pay out the increased payment for next year, and have enough left over to help towards future increases in payments. (Note  that we are assuming that R > I. If R < I, a perpetuity cannot be created.)  Thus, suppose that we choose p such that P*(1+R) - p = P*(1+I)   Multiplying this equation by (1+I), we have [P(1+I)]*(1+R) - [p*(1+I)] = P*(1+I)^2 In words, at the start of next year, the investment is P*(1+I) and the return less the increased payout of p*(1+I) leaves an investment of P*(1+I)^2 for the following year.  Each year, the payment and the amount to be invested for the following year increase by a factor of (1+I). Solving P*(1+R) - p = P*(1+I) for p, we get  p = P*(R-I)  as the initial perpetuity payment and the payment increases by a factor (1+I) each year.  The initial investment is P and it also increases by a factor of (1+I) each year. In later years, the investment is P*(1+I)^n at the start of the year, the payment is p*(1+I)^n and the amount invested for the next year is P*(1+I)^{n+1}. This is the same result as obtained by the OP but written in terms that I can understand, that is, without the financial jargon about discount rates, gradients, PV, FV and the like. This is the same as any case where income is variable.  How do you deal with the months where expected cash flows are lower than projected? When I got married, my wife was in the habit of allocating money to be spent in the current month from income accrued during the previous month.  This is slightly complicated because we account for taxes (and benefit expenses) withheld in the current months' paychecks as current expenses, but we allocate the gross income from that check to the following month for spending. The benefit of spending only money made during the previous month is that income shocks are less shocking.  I was working for a start-up and they missed payroll that normally arrived on the first of the month.  Most of my co-workers were calling the bank in a panic to avoid over-draft fees with their mortgage payments, but my mortgage payment was already covered.  Similarly, when the same start-up had a reduction in force on the first day of a new quarter, I didn't have to pull any money from savings during the 3 weeks I was unemployed. In the end, you're going to have to allocate money to the budget based on the actual income--which is lower than your expectations.  What part of the budget should fairly be reduced is a question you and your wife will have to figure out. If I is the initial deposit, P the periodic deposit, r the rent per period, n the number of periods, and F the final value, than we can combine two formulas into one to get the following answer: F = I*(1+r)n + P*[(1+r)n-1]/r In this case, you get V = 1000*(1.05)20 + 100*[(1.05)20-1]/0.05 = 5959.89 USD. Note that the actual final value may be lower because of rounding errors. "Provide you are willing to do a bit of work each month, you should apply for a ""rewards checking"" account.  Basically these accounts require you to set up direct deposit (can be any amount and your employer can easily deposit $25 into one account and the rest into another if you like).  They also require you to use your debit card attached to the account (probably about 10 times per month). Check out the list on the fatwallet finance forum.  Right now the best accounts are earning over 4%." In addition to the answer from CQM, let me answer your 'am I missing anything?' question. Then I'll talk about how your approach of simplifying this is making it both harder and easier for you. Last I'll show what my model for this would look like, but if you aren't capable of stacking this up yourself, then you REALLY shouldn't be borrowing 10,000 to try to make money on the margin. Am I missing anything? YES. You're forgetting (1) taxes, specifically income tax, and (2) sales commissions//transaction fees.  On the first: You have not considered anything in your financial model for taxes. You should include at least 25% of your expected returns going to taxes, because anything that you buy... and then sell within 12 months... is taxed as income. Not capital gains. On the second: you will incur sales commissions and/or transaction fees depending on the brokerage you are using for your plan. These tend to vary widely, but I would expect to spend at least $25 per sale. So if I were building out this model I would think that your break-even would have to at least cover: monthly interest + monthly principal payment income tax when sold commissions and broker's fees every time you sell holdings On over-simplifying: You have the right idea with thinking about both interest and principal in trying to sketch this out. But as I mentioned above, you're making this both harder and easier for yourself. You are making it harder because you are doing the math wrong. The actual payment for this loan (assuming it is a normal loan) can be found most easily with the PMT function in Excel: =PMT(rate,NPER,PV,FV)... =PMT(.003, 24, -10000, 0). That returns a monthly payment  (of principal + interest) of 432.47.  So you actually are over-calculating the payment by $14/month with your ballpark approach. However, you didn't actually have all the factors in the model to begin with, so that doesn't matter much.  You are making it artificially easier because you have not thought about the impact of repaying principal. What I mean is this--in your question you indicate:  I'm guessing the necessary profit is just the total interest on this loan = 0.30%($10000)(24) = $720 USD ? So I'll break even on this loan - if and only if - I make $720 from stocks over 24 months (so the rate of return is 720/(10000 + 720) = 6.716%). This sounds great-- all you need is a 6.716% total return across two years. But, assuming this is a normal loan and not an 'interest-only' loan, you have to get rid of your capital a little bit at a time to pay back the loan. In essence, you will pay back 1/3 of your principal the first year... and then you have to keep making the same Fixed interest + principal payments out of a smaller base of capital.  So for the first few months you can cover the interest easily, but by the end you have to be making phenomenal returns to cover it.  Here is how I would build a model for it (I actually did... and your breakeven is about 1.019% per month. At that outstanding 12.228% annual return you would be earning a whopping $4.) At least as far as the variables are concerned, you need to be considering: Your current capital balance (because month 1 you may have $10,000 but month 2 you have just 9,619 after paying back some principal).  Your rate of return (if you do this in Excel you can play with it some, but you should save the time and just invest somewhere else.) Your actual return that month (rate of return * existing capital balance).  Loan payment = 432 for the parameters you gave earlier.  Income tax = (Actual Return) * (.25). With this kind of loan, you're not actually making enough to preserve the 10,000 capital and you're selling everything you've gained each month.  Commission = ($25 per month) ... assuming that covers your trade fees and broker commissions. I guarantee you that this is not the deal breaker in the model, so don't get excited if you think I'm over-estimating this and you realize that Scottrade or somewhere will let you have trades at $7.95 each.   Monthly ending balance == next month's starting capital balance.  Stack it all up in Excel for 24 months and see for yourself if you like. The key thing you left out is that you're repaying each month out of capital that you'd like to use to invest with. This makes you need much higher returns.  Even if your initial description wasn't clear and this is an interest-only loan, you're still looking at a rate of about 7.6% annually that you need to hit in order to just break even on the costs of holding the loan and transferring your gains into cash. "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." "Trying to figure out how much money you have available each day sounds like you're making this more complicated than it needs to be. Unless you're extremely tight and you're trying to squeeze by day by day, asking ""do I have enough cash to buy food for today?"" and so on, you're doing too much work. Here's what I do. I make a list of all my bills. Some are a fixed amount every month, like the mortgage and insurance premiums. Others are variable, like electric and heating bills, but still pretty predictable.  Most bills are monthly, but I have a few that come less frequently, like water bills in my area come every 3 months and I have to pay property taxes twice a year. For these you have to calculate how much they cost each month. Like for the water bill, it's once every 3 months so I divide a typical bill by 3. Always round up or estimate a little high to be safe. Groceries are a little tricky because I don't buy groceries on any regular schedule, and sometimes I buy a whole bunch at once and other times just a few things. When groceries were a bigger share of my income, I kept track of what I spent for a couple of months to figure out an average per month. (Today I'm a little richer and I just think of groceries as coming from my spending money.) I allocate a percentage of my income for contributions to church and charities and count this just like bills. It's a good idea to put aside something for savings and/or paying down any outstanding loans every month. Then I add these up to say okay, here's how much I need each month to pay the bills. Subtract that from my monthly income and that's what I have for spending money. I get paid twice a month so I generally pay bills when I get paid. For most bills the due date is far enough ahead that I can wait the maximum half a month to pay it. (Worst case the bill comes the day after I pay the bills from this paycheck.)  Then I keep enough money in my checking account to, (a) Cover any bills until the next paycheck and allow for the particularly large bills; and (b) provide some cushion in case I make a mistake -- forget to record a check or make an arithmetic error or whatever; and (c) provide some cushion for short-term unexpected expenses. To be safe, (a) should be the total of your bills for a month, or as close to that as you can manage. (b) should be a couple of hundred dollars if you can manage it, more if you make a lot of mistakes. If you've calculated your expenses properly and only spend the difference, keeping enough money in the bank should fall out naturally. I think it's a lot easier to try to manage your money on a monthly basis than on a daily basis. Most of us don't spend money every day, and we spend wildly different amounts from day to day. Most days I probably spend zero, but then one day I'll buy a new TV or computer and spend hundreds.  Update in response to question What I do in real life is this: To calculate my available cash to spend, I simply take the balance in my checking account -- assuming that all checks and electronic payments have cleared. My mortgage is deducted from my checking every month so I post that to my checking a month in advance. I pay a lot of things with automatic charges to a credit card these days, so my credit card bills are large and can't be ignored. So subtract my credit card balances. Subtract my reserve amount. What's left is how much I can afford to spend. So for example: Say I look at the balance in my checkbook today and it's, say, $3000. That's the balance after any checks and other transactions have cleared, and after subtracting my next mortgage payment. Then I subtract what I owe on credit cards. Let's say that was $1,200. So that leaves $1,800. I try to keep a reserve of $1,500. That's plenty to pay my routine monthly bills and leave a healthy reserve. So subtract another $1,500 leaves $300. That's how much I can spend. I could keep track of this with a spreadsheet or a database but what would that gain? The amount in my checking account is actual money. Any spreadsheet could accumulate errors and get farther and farther from accurate values. I use a spreadsheet to figure out how much spending money I should have each month, but that's just to use as a guideline. If it came to, say, $100, I wouldn't make grandiose plans about buying a new Mercedes. If it came to $5,000 a month than buying a fancy new car might be realistic. It also tells me how much I can spend without having to carefully check balances and add it up. These days I have a fair amount of spending money so when, for example, I recently decided I wanted to buy some software that cost $100 I just bought it with barely a second thought. When my spending money was more like $100 a month, lunch at a fast food place was a big event that I planned weeks in advance. (Obviously, I hope, don't get stupid about ""small amounts"". If you can easily afford $100 for an impulse purchase, that doesn't mean that you can afford $100 five times a day every day.) Two caveats: 1. It helps to have a limited number of credit cards so you can keep the balances under control. I have two credit cards I use for almost everything, so I only have two balances to keep track of. I used to have more and it got confusing, it was easy to lose track of how much I really owed, which is a set up for getting in trouble." "I will add another point to ChrisinEdmonton's answer... I recognize that this is perhaps appropriate as a comment--or maybe 1/2 of an answer, but the comment formatting is inadequate for what I want to say.  The magic formula that you need to understand is this:  (Capital Invested) * (Rate of Return) = (Income per Period) When ChrisinEdmonton says that you need $300,000, he is doing some basic algebra... (Capital Required) = (Income per Period) / (Rate of Return)  So if you're looking at $12,000 per year in passive income as a goal, and you can find a ""safe"" 4% yield, then what ChrisinEdmonton did is:  $12,000 / 0.04 = $300,000 You can use this to play around with different rates of return and see what investment options you can find to purchase. Investment categories like REITs will risk your principal a little more, but have some of the highest dividend yields of around 8%--12%. You would need $100,000--$150,000 at those yields.  Some of the safest approaches would be bonds or industrial stocks that pay dividends. Bonds exist around 3%--4%, and industrial dividend stocks (think GE or UTX or Coca Cola) tend to pay more like 2%-3%.  The key point I'm trying to make is that if you're looking for this type of passive income, I recommend that you don't plan on the income coming from gains to the investment... This was something that ChrisinEdmonton wasn't entirely clear about. It can be complicated and expensive to whittle away at a portfolio and spend it along the way." This is basically a math problem. It depends on the pension benefits, the lump sum, and the chance that the company doesn't honor its pension plan. If you're willing to share the first 2 and the company name, it's possible to roughly figure out the odds of the third if your company has bonds or CDS. Maybe some bored analyst would do it for you here, or you could probably hire a financial advisor for an hour or 2 to figure it out.