PMT

[Guest]

I know the PMT function. With 3 mandatory arguments it can provide the
monthly payment amount. I would like to know the mathematical steps it
performs to arrive at the monthly payment amount.

 

[Shaz]

The PMT function is an annuity, you find tons of material on annuities
online.
In any case thjis is the annuity formula:

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

where r is the interest rate an n is the number of periods. HOJw do you
arrive to it?, well the PV of an infinite series of payments PMT =

PV= PMT/r

now you need to substract the value of the anunnuity from n to infinity
which is:

PV= (PMT/r)*(1/(1+r)^n) this is the PV of series form n to infinity

You are left with:

PV(annuity) = PMT/r - PMT/r*(1/(1+r)^n) which leads to the formula
above.

regards,

S.