hey guys, i am building an excel sheet to keep track of my private investments and my problem is this:

I will invest an amount x per month, increasing every couple years as my salary increases, at interest rate r, under continuous compounding for t=40 years.

what I got so far:

Future Value = [e^(r/12*12*40)] * [x/(r/12)*(1-e^(-r/12)*40*12)]

this formula works, however, it does not take into account that amount X will likely increase in the future. i think i have to multiply x with another e-expression but i cant figure out how exactly.

pls help

This post was edited by annieleonhardt on Sep 14 2013 08:00pm

Well if you can come up with a function to model the amount you will be investing (as a function of time), you can replace x with it. Of course only you can come up with that function since no one else knows your plans.

This post was edited by Azrad on Sep 14 2013 11:52pm

yes, but assuming the amount would be 300 per month in the beginning and increase by 3% per year (on average) x has to be something like 300e^"something" and i dont know how to include the 3 percent

is it compound interest or annual?

http://en.wikipedia.org/wiki/Compound_interest

http://en.wikipedia.org/wiki/Interest

he specified continuous

if you want to increase in amount per year, what you're looking at is either geometric (what you want) or arithmetic growth.

Therefore, let A=current investment right now, you will then find

1. fv given annuity A at interest rate r for t=40
2. fv given geometric series with A, g=0.03, and interest rate r (assuming you grow every period, which is not true I guess)

The just add.

Best way of evaluating though for excel is to just npv the entire cashflow and find the effective monthly interest rate under continuous compounding and use that as your discount rate.

ie, suppose r=5%, then reffectivemontly = e(0.05/12)-1=0.00417535929

edit:

so suppose you have A=100, then in cell say A1 you put 100, then you have say a constant g = 0.03

then A2 you will have if(growthismonth,A1*(1+g),A1)

where growthismonth is a way of evaluating whether or not you choose to be putting in more money this time around.

This post was edited by madeinchinars on Sep 15 2013 02:50pm