# How to calculate future value with a monthly payment?

So I went to the investor.gov website and got to playing around with one of their compound interest calculators and entered the following: A =$1000, PMT=$150(monthly), t=45 years, r=8%, and it's being compounded monthly. The calculator said the future value would be $827,344.58 I would like to know what formula was used to get this result and how does the calculator know when I will make my deposit? Beginning of the month or end of the month? Any help figuring out how the calculator got this answer would be appreciated! Thanks! #### DenisB What you have here is equivalent to a savings account that'll look like this: Code: MTH AMOUNT INTEREST BALANCE 0 1000.00 1 150.00 6.67 1156.67 2 150.00 7.71 1314.38 3 150.00 8.76 1473.14 .... 538 150.00 5403.81 816125.64 539 150.00 5440.84 821716.48 540 150.00 5478.10 827344.58 Interest calculated this way (month 3 as example): 1314.38 * .08 / 12 = 8.76 I'm watching a football game...so I'll let someone else give you the 2 formulas required!!! #### Walagaster MHF Helper The formula is$$FV =P\left(\frac{(1+r)^n-1}{r}\right)+ A(1+r)^n$$ where$P=150,~r=\frac{.08}{12},~A=1000,~n=45*12 = 540$. #### slapmaxwell1 Thanks!! #### slapmaxwell1 Thanks for the formulas!!! #### DenisB If (as example) you wanted to know what the monthly deposits contribute to the 827344.58, you'd simply deduct the future value of the initial$1000:
827344.58 - 1000*(1 + .08/12)^540
= 827344.58 - 36163.60
= 791180.98

On your "beginning or end of month" question,
the calculator simply needs to be able to do both,
and should contain a "button!" labelled "immediate or deferred?"

YOKAY?