Increasing payment in future value formula?

[Guest]

Can I use an increasing payment in a future value formula in 2002 Excel?

 

[Fred Smith]

No you can't. FV assumes a constant payment. The formula to calculate the
future value of a payment invested at i% increasing j% every period is:

FV=PMT * ((1+i)^n - (1+j)^n) / (i-j)

 

[Guest]

Yes you can but you need to write it yourself. the Present Value function for
increasing payments is:

PV*(1+r)^n + pmt*((1+r)^n - (1+i)^n))/(r-i) + FV = 0

where:
i = rate of pmt increase per period
r = interest rate per period
n = number of payment periods
pmt = payment made each period
FV = Future value after last paytment is made

If payment is fixed, or i=0, then the formula becomes the familiar

PV*(1+r)^n + pmt*((1+r)^n - 1)/r + FV = 0

as documented in the excel PV function

Payment at month j is:

pmt*(1+i)^j

Let me know if you have any questions or comments. I would be glad to show
how I derived this formula