Need a formula to determine monthly payments received at time t if I'm reinvesting my returns

I need a formula for how much money I will be receiving monthly and how much I will have in total for any time t (in months). The following is my scenario: I will be investing \$900 monthly into a 3 year investment with a return of 10%. I plan to reinvest my monthly returns. For Example:

Month 1 : receive \$0 input:\$900 invest \$900

(900*1.10 =990. 990/36 months = \$27)

M2: receive: \$27 input: \$900 invest \$927

(927*1.1/36= 28)

M3: receive: \$27 + \$28 input: \$900 invest \$955

And so on... At month 36 I should have a monthly payment for months 1-36 plus my 900 to invest. At month 37 however, I will no longer receive my month 1 payments as it's 3 years will have matured and will be done. That's where it all starts to get tricky for me. I'm having trouble putting together a generic formula for this investment scheme. I have a masters in math but no business/investing experience so I'm a little lost. Ignoring inflation and the chance that some investments may fall through how much money will I be receiving monthly at time t? How much will I have in total?

Please read through before answering. Other sites I've asked this question the only response I get is to use the compound interest formula. I'm fairly certain that doesn't apply in my case. Thank you!

• Is 10% the three year return, or did you mean 10%/yr? Nov 12, 2013 at 17:56
• The three year return I believe. Like I invest \$900 and get back \$990 but that \$990 is paid evenly over the course of 3 years in installments of \$27.50. Nov 12, 2013 at 18:27
• If you give me \$900 and I return 36 payments of \$27.50, your return is closer to 5%. So long as you are clear on the three variables, we can tell you how to solve the 4th. Your scenario is still not clear to me, what cash return does that second \$900 deposit get? Nov 12, 2013 at 18:41
• Thank you so much for trying to help. I'm sorry for being so unclear. The money added into the second \$900 is supposed to be the first monthly payment from the first \$900. So if I invest \$900 and get back \$27.50 per month, the following month I will take that \$27.50, add another \$900 and invest \$927.50 at a return of 10%. This would result in a new monthly payment of \$28.34. In month 2 I take my second \$27 payment and my first \$28 payment and add in a new \$900 to invest \$955 at the same return of 10%. The return would always be 10%. Hope that helped. Thanks again Nov 12, 2013 at 21:26
• You may be clear. I am getting old and English sometimes fails me. A rate has to be for a specific period of time. 10% over 3 years is just over 3% per year. If that's what you mean, that's fine, it's just an odd way to approach a problem. I am used to an annual rate or a rate per compounding period, such as .5% per month compounded. Nov 13, 2013 at 2:54

How does compounding of annual interest work? answers this question. It's not simple compound interest. It's a time value of money calculation similar to mortgage calculations. Only the cash flow is the other way, a 'deposit' instead of 'payment'.

When using a finance calculator such as the TI-BA35 (Note, it's no longer manufactured, but you can find secondhand. It was the first electronic device I ever loved. Seriously) you enter PV (present value) FV (future value) Int (the interest rate) nPer (number of periods) PMT (payment).

For a mortgage, there's a PV, but FV = \$0. For you, it's reversed. PMT on this model is a positive number, for you it's negative, the amount you deposit. You also need to account for the fact that a mortgage is paid on day 31, but you start deposits on Day 1. See the other answer (I linked at start) for the equations.

• Thank you! I'm currently at work. Once I get home I will read through your link, study up and then see if I understand/have resolved my issue. Nov 12, 2013 at 21:31

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.

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.

• It was your answer at the other question that had it fresh in my mind. I know we can help this OP, but I am still not understanding his question 100%. Nov 12, 2013 at 20:46
• At the end of month 36 there will still be 35 investment units that will be throwing off a decreasing amount of income for the next 36 months. Nov 12, 2013 at 20:59