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
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. "The short of it is that bonds are valued based on a fundamental concept of finance called the ""time value of money"". Stated simply, $100 one year from now is not the same as $100 now. If you had $100 now, you could use it to make more money and have more than $100 in a year. Conversely, if you didn't invest it, the $100 would not buy as much in a year as it would now, and so it would lose real value. Therefore, for these two benefits to be worth the same, the money received a year from now must be more than $100, in the amount of what you could make with $100 if you had it now, or at least the rate of inflation. Or, the amount received now could be less than the amount recieved a year from now, such that if you invested this lesser amount you'd expect to have $100 in a year. The simplest bonds simply pay their face value at maturity, and are sold for less than their face value, the difference being the cost to borrow the cash; ""interest"". These are called ""zero-coupon bonds"" and they're around, if maybe uncommon. The price people will pay for these bonds is their ""present value"", and the difference between the present value and face value determines a ""yield""; a rate of return, similar to the interest rate on a CD. Now, zero-coupon bonds are uncommon because they cost a lot. If I buy a zero-coupon bond, I'm basically tying up my money until maturity; I see nothing until the full bond is paid. As such, I would expect the bond issuer to sell me the bond at a rate that makes it worth my while to keep the money tied up. So basically, the bond issuer is paying me compound interest on the loan. The future value of an investment now at a given rate is given by FV = PV(1+r)t. To gain $1 million in new cash today, and pay a 5% yield over 10 years, a company or municipality would have to issue $1.629 million in bonds. You see the effects of the compounding there; the company is paying 5% a year on the principal each year, plus 5% of each 5% already accrued, adding up to an additional 12% of the principal owed as interest. Instead, bond issuers can offer a ""coupon bond"". A coupon bond has a coupon rate, which is a percentage of the face value of the bond that is paid periodically (often annually, sometimes semi-annually or even quarterly). A coupon rate helps a company in two ways. First, the calculation is very straightforward; if you need a million dollars and are willing to pay 5% over 10 years, then that's exactly how you issue the bonds; $1million worth with a 5% coupon rate and a maturity date 10 years out. A $100 5% coupon bond with a 10-year maturity, if sold at face value, would cost only $150 over its lifetime, making the total cost of capital only 50% of the principal instead of 62%. Now, that sounds like a bad deal; if the company's paying less, then you're getting less, right? Well yes, but you also get money sooner. Remember the fundamental principle here; money now is worth more than money later, because of what you can do with money between now and later. You do realize a lower overall yield from this investment, but you get returns from it quickly which you can turn around and reinvest to make more money. As such, you're usually willing to tolerate a lower rate of return, because of the faster turnaround and thus the higher present value. The ""Income Yield %"" from your table is also referred to as the ""Flat Yield"". It is a very crude measure, a simple function of the coupon rate, the current quote price and the face value (R/P * V). For the first bond in your list, the flat yield is (.04/114.63 * 100) = 3.4895%. This is a very simple measure that is roughly analogous to what you would expect to make on the bond if you held it for one year, collected the coupon payment, and then sold the bond for the same price; you'd earn one coupon payment at the end of that year and then recoup the principal. The actual present value calculation for a period of 1 year is PV = FV/(1+r), which rearranges to r = FV/PV - 1; plug in the values (present value 114.63, future value 118.63) and you get exactly the same result. This is crude and inaccurate because in one year, the bond will be a year closer to maturity and will return one less coupon payment; therefore at the same rate of return the present value of the remaining payout of the bond will only be $110.99 (which makes a lot of sense if you think about it; the bond will only pay out $112 if you bought it a year from now, so why would you pay $114 for it?). Another measure, not seen in the list, is the ""simple APY"". Quite simply, it is the yield that will be realized from all cash flows from the bond (all coupon payments plus the face value of the bond), as if all those cash flows happened at maturity. This is calculated using the future value formula: FV = PV (1+r/n)nt, where FV is the future value (the sum of the face value and all coupon payments to be made before maturity), PV is present value (the current purchase price), r is the annual rate (which we're solving for), n is the number of times interest accrues and/or is paid (for an annual coupon that's 1), and t is the number of years to maturity. For the first bond in the list, the simple APY is 0.2974%. This is the effective compound interest rate you would realize if you bought the bond and then took all the returns and stuffed them in a mattress until maturity. Since nobody does this with investment returns, it's not very useful, but it can be used to compare the yield on a zero-coupon bond to the yield on a coupon bond if you treated both the same way, or to compare a coupon bond to a CD or other compound-interest-bearing account that you planned to buy into and not touch for its lifetime. The Yield to Maturity, which IS seen, is the true yield percentage of the bond in time-valued terms, assuming you buy the bond now, hold it to maturity and all coupon payments are made on time and reinvested at a similar yield. This calculation is based on the simple APY, but takes into account the fact that most of the coupon payments will be made prior to maturity; the present value of these will be higher because they happen sooner. The YTM is calculated by summing the present values of all payments based on when they'll occur; so, you'll get one $4 payment a year from now, then another $4 in two years, then $4 in 3 years, and $104 at maturity. The present value of each of those payments is calculated by flipping around the future value formula: PV = FV/(1+r)t. The present value of the entire bond (its current price) is the sum of the present value of each payment: 114.63 = 4/(1+r) + 4/(1+r)2 + 4/(1+r)3 + 104/(1+r)4. You now have to solve for r, which is difficult to isolate; the easiest way to find the rate with a computer is to ""goal seek"" (intelligently guess and check).  Based on the formula above, I calculated a YTM of .314% for the first bond if you bought on Sept 7, 2012 (and thus missed the upcoming coupon payment). Buying today, you'd also be entitled to about 5 weeks' worth of the coupon payment that is due on Sept 07 2012, which is close enough to the present day that the discounted value is a rounding error, putting the YTM of the bond right at .40%. This is the rate of return you'll get off of your investment if you are able to take all the returns from it, when you receive them, and reinvest them at a similar rate (similar to having a savings account at that rate, or being able to buy fractional shares of a mutual fund giving you that rate)." While the rest of the answers seem to be focusing on the parenting strategies around giving children an allowance, I'd like to address how to accomplish that.   I think the best most reasonable way to just to supply him with a checking and savings account at whichever bank you use.  Most reasonable banks will have some form of no-fee account for minors/young people; others will waive fees if you have it paired with your account.  Whatever way to can swing it, get the kid an account he can deposit/withdraw from and that is free of any additional services.  He doesn't need to learn the pain of overdrafts or random fees yet.  Then, just set up a recurring weekly/monthly transfer to the account, and let him determine his own allocation to savings and spending.  If he can manage it online, even better, that's a far more useful skill than knowing how to fill out a deposit slip at the bank. If they short the contract, that means, in 5 months, they will owe if the price goes up (receive if the price goes down) the difference between the price they sold the future at, and the 3-month Eurodollar interbank rate, times the value of the contract, times 5. If they're long, they receive if the price goes up (owe if the price goes down), but otherwise unchanged. Cash settlement means they don't actually need to make/receive a three month loan to settle the future, if they held it to expiration - they just pay or receive the difference.  This way, there's no credit risk beyond the clearinghouse. The final settlement price of an expiring three-month Eurodollar futures (GE) contract is equal to 100 minus the three-month Eurodollar interbank time deposit rate. 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. Use TWIRR (aka TWRR). Time Weighted rate of return. It's sort of the opposite of XIRR. XIRR results change dramatically depending on the timing of the cashflows. It might be useful to also model returns that are unaffected by the timing. This is how funds report returns, and this number allows you to compare to funds and indices. During periods of steady deposits, XIRR will continually understate performance. And in retirement, when you have steady withdrawals, XIRR will overstate. TWRR is talked about here: http://www.dailyvest.com/PRR/prr_calcmethods.aspx#twrr I've made a simple spreadsheet that you can use as a starting point, if you like: http://moosiefinance.com/static/models/spreadsheets.html (top entry in the list) "I don't have a formula for anything like this, but it is important to note that the ""current value"" of any asset is really theoretical until you actually sell it. For example, let's consider a house.  You can get an appraisal done on your house, where your home is inspected, and the sales of similar houses in your area are compared.  However, this value is only theoretical.  If you found yourself in a situation where you absolutely had to sell your house in one week, you would most likely have to settle for much less than the appraised value. The same hold true for collectibles.  If I have something rare that I need cash for immediately, I can take it to a pawn shop and get cash.  However, if I take my time and locate a genuinely interested collector, I can get more for it. This is comparable to someone who holds a significant percentage of shares in a publicly held corporation.  If the current market value of your shares is $10 million, but you absolutely need to sell your entire stake today, you aren't going to get $10 million.  But if you take your time selling a little at a time, you are more likely to get much closer to this $10 million number. A ""motivated seller"" means that the price will drop." So would it be more sensible to park the money in 3 separate fixed deposits created each month or to invest this money as usual in debt and mutual funds and instead just liquidate the recurring deposit and use it to pay my taxes in July? Most taxes would already have been paid by March 31. So what you are talking here is less than Rs 10,000/- of taxes. The optimization you are looking at is very small and you are better of choosing one that is more convenient.