How to calculate future value with a monthly payment?

Aug 2009
356
0
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!
 
Feb 2015
2,255
510
Ottawa Ontario
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
Apr 2018
230
146
Tempe, AZ
The formula is$$
FV =P\left(\frac{(1+r)^n-1}{r}\right)+ A(1+r)^n$$
where $P=150,~r=\frac{.08}{12},~A=1000,~n=45*12 = 540$.
 
Feb 2015
2,255
510
Ottawa Ontario
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?