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.
"Figure out how much money you earn, what you spend it on, and how that will change when you have kids (will one of you stay at home? if not, how much will daycare cost and how do you finance the first few month when your child is still too young for daycare?) You will usually plan to spend your current Kaltmiete (rent without utilities) on your mortgage (the Darlehen that is secured by your house) - keep in mind though that a house usually has a higher utility cost than an appartment. When you've figured out what you can save/pay towards a house now and how that will change when you have kids, you can go on to the next step. If you don't want to buy now but want to commit to saving up for a house and also want to secure today's really low interest rates, consider getting a ""Bausparvertrag"".  I didn't find a good translation for Bausparvertrag, so here is a short example of how it works: You take a building saving sum (Bausparsumme) of 150000€ with a savings goal (Sparziel) of 50000€ (the savings goal is usually between 20% and 50% of the sum) and then you make monthly payments into the Bausparvertrag until you reach the savings goal at which point you can take out your savings and a loan of 100000 € (or whatever your difference between the Bausparsumme and Sparziel is). If you're living in an expenisve area, you're likely to need more than 150000 but this is just an example. Upsides: Downsides: If you decide to buy sooner, you can also use your Bausparvertrag to refinance later. If you have a decent income and a permanent job, then ask your bank if they would consider financing your house now. To get a sense of what you'll be able to afford, google ""wie viel Haus kann ich mir leisten"" and use a few of the many online calculators. Remember that these websites want to sell you on the idea of buying a house instead of paying rent, so they'll usually overestimate the raise in rents - repeat the calculation with rent raise set to 0% to get a feeling for how much you'll be able to afford in today's money. Also, don't forget that you're planning to get children, so do the calculation with only one income, not two, and add the cost of raising the kids to your calculation. Once you've decided on a property, shop around a bit at different banks to get the best financing. If you decide to buy now (or soon), start looking at houses now - go to model homes (Musterhäuser) to find out what style of house you like - this is useful whether you want to buy an existing house or build a new one. If buying an existing house is an option for you, start visiting houses that are on sale in your area in order to practice what to ask and what to look for. You should have a couple of visits under your belt before you really start looking for the one you want to buy. Once you're getting closer to buying or making a contract with a construction company, consider getting an expert ""Bausachverständiger"". When buying an existing house they can help you estimate the price and also estimate the renovation cost you'll have to factor in for a certain house (new heating, better insulation, ...). When building a new house they can advise you on the contract with the construction company and also examine the construction company's work at each major step (Zwischenabnahme). Source: Own experience." "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." As I understand it, US federal gift tax doesn't kick in at all until one person gives more than about $14,000 in a single year. (So a couple can give someone $28,000.) If you want to give more than that in a lump sum while avoiding gift tax, one workaround is to structure it as an intra-family loan. Basically, you write (and formally register) a loan for the amount, then gift them with up to the limit for them to pay off that loan. The IRS requires that you charge interest on this loan, but the rates are pretty minimal and of course you can incorporate that in the gift. The downside is that the interest income you're required to take is taxable, but that's a comparitively small sum. (On the other hand, if the loan is a mortgage against real property, and properly filed as such, the interest paid may be deductable for the person you're giving the money to.) Doing this properly requires a tax accountant or lawyer who has a clue about the right legalese to make it work. However, there are starting to be some services which specialize in this, doing it for a fixed fee. I used one of those recently, which is why I'm somewhat familiar with this process; they made it about as much of a fill-out-the-forms process as they could, but it still took a few weeks for me to figure out which options were best for my needs. The monthly repayments of the initial $ 300,000 loan can be calculated using this formula:  source: Finance Formulas The monthly payment is It is not readily apparent how the formula works, but it is derived by induction from this summation, in which the sum of the discounted future payments are set equal to the present value of the loan:  For the second part of the question, reinvestments are stopped after 9 months, after four investments of $ 26,374.77 * 3 = $ 79,124.31.  And presumably each loan is repaid in 3 years, since 45 - 9 = 36 months. Calculating the repayments for these loans: The total returned for all four loans is: You could use  the Gordon growth model implied expected return: P = D/(r-g) --&gt; r = D/P (forward dividend yield) + g (expected dividend growth). But obviously there is no such thing as a good market return proxy. First let's define some terms. Your accrued benefit is a monthly benefit payable at your normal retirement age (usually 65). It is usually a life-only benefit but may have a number of years guaranteed or may have a survivor piece. It is defined by a plan formula (ie, it is a defined benefit). A lump sum is how much that accrued benefit is worth right now. Lump sums are based on applicable interest rates and mortality tables specified by the IRS (interest rates are released monthly, mortality annually). Your plan can either use the same interest rates for a whole year, or they can use new ones each month. Affecting your lump sum is whether your accrued benefit is payable now (immediately, you are age 65), or later (deferred, you are now age 30). For example, instead of being paid an annuity assume you are paid just one payment of $1,000 on your 65th birthday. The lump sum of that for a 65 year old would be $1,000 since there would be no interest discount, and no chance of dying before payment. For a 30 year old, at 4% interest the lump sum would be about $237 (including mortality discount). At age 36 the lump sum is $246. So the lump sum will get bigger just because you get older. Very important is the interest discount. At age 30 in the example, 2% interest would produce a $467 lump sum. And at 6% $122. The bigger the rate, the smaller the lump sum because interest helps an amount now grow bigger in the future. To complicate things, since 2008 the IRS bases lump sums on 3 different interest rates. The monthy annuity payments made within 5 years of the lump sum date use the 1st rate, past 5 and within 20 years use the 2nd rate, and past that use the 3rd rate. Since you are age 30, all of your monthly annuity payments would be made after 20 years, so that makes it simple since we'll only have to look at the 3rd rate. When you reach age 45 the 2nd rate will kick in. Here is the table of interest rates published by the IRS: http://www.irs.gov/Retirement-Plans/Minimum-Present-Value-Segment-Rates You'll find your rates above on the 2013 line for Aug-12. That means your lump sum is being made in 2013 and it is being based on the month August 2012. Most likely your plan will use the same rates for its entire plan year. But what is your plan year? If it is the calendar year, then you would have a 5 month lookback for the rates. But if is a September to August plan year with a 1 month lookback, the rates would have changed between August and September. Your August lump sum would be based on 4.52%, your September on would be based on 5.58% (see the All line for Aug-13). For comparison, a 30 year old with a $100 annuity payable at age 65 would have a lump sum value of $3,011 at 4.52%, but a lump sum value of $1,931 at 5.58%. The change in your accrued benefit by month will obviously have some impact on the lump sum value, but not as much as the change in interest rates if there is one. The amount they actually contribute to the plan has nothing to do with the value of the lump sum though. The equation is the same one used for mortgage amortization.  You first want to calculate the PV (present value) for a stream of $50K payments over 20 years at a10% rate.  Then that value is the FV (future value) that you want to save for, and you are looking to solve the payment stream needed to create that future value. Good luck achieving the 10% return, and in knowing your mortality down to the exact year. Unless this is a homework assignment, which need not reflect real life.  Edit - as indicated above, the first step is to get that value in 20 years:  The image is the user-friendly entry screen for the PV calculation. It walks you though the need to enter rate as per period, therefore I enter .1/12 as the rate. The payment you desire is $50K/yr, and since it's a payment, it's a negative number. The equation in excel that results is: =PV(0.1/12,240,-50000/12,0) and the sum calculated is $431,769 Next you wish to know the payments to make to arrive at this number:  In this case, you start at zero PV with a known FV calculated above, and known rate. This solves for the payment needed to get this number, $568.59 The excel equation is: =PMT(0.1/12,240,0,431769) Most people have access to excel or a public domain spreadsheet application (e.g. Openoffice). If you are often needing to perform such calculations, a business finance calculator is recommended. TI used to make a model BA-35 finance calculator, no longer in production, still on eBay, used.  One more update- these equations whether in excel or a calculator are geared toward per period interest, i.e. when you state 10%, they assume a monthly 10/12%. With that said, you required a 20 year deposit period and 20 year withdrawal period. We know you wish to take out $4166.67 per month. The equation to calculate deposit required becomes - 4166.67/(1.00833333)^240= 568.59  HA! Exact same answer, far less work. To be clear, this works only because you required 240 deposits to produce 240 withdrawals in the future. 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.