Is there any other formula for discounting a money amount

[DexterOnline]

For discrete compounding, the formula often quoted in textbooks to discount a money amount is given by

PV = FV (1+i)^-n

where

i is the interest rate

n is the number of periods

FV is the amount due in future

PV is the discounted value at present

For continuous compounding, the formula often quoted in textbooks to discount a money amount is given by

PV = FV e^-in

where

e is the mathematical constant that is called Euler's E

Are there any other formula(s) that may be used that produce the same results as the two formulas mentioned above

 

[Ishuda]

What you have presented is the formula for the present value for (a) compound interest compounded (assumed) yearly at an annual interest rate of i for a period of n years
PV = FV (1+i)^-n
and (b) compound interest compounded continuously
PV = FV e^-in.
The amounts would be different.

You can also have different compounding periods, i.e. daily, weekly (although I haven't seen that), monthly, quarterly, etc. If you let t be the number of whole periods in a year and the interest rate is compounded t times per year, the present value is again a different number given by
PV = FV \(\displaystyle (1 + \frac{i}{t})^{-t\, n}\)

If you play with the formulas a bit and note that
\(\displaystyle (1 + \frac{i}{t})^{t\, n} = [(1 + \frac{1}{t/i})^{t/i}]^{i\, n} \)
we see that
\(\displaystyle \lim_{t \to \infty} [(1 + \frac{1}{t/i})^{t/i}] = e\)

 

[DexterOnline]

What you show is only an extension of the two formulas I have given

It does not necessarily matter if we include compounding, the basic formulas stay the same

What I am asking is are there any equivalent formulas or say functions that have the same domain and range as the two functions given