1. The future value of a single cash flow.
For yearly compounding:
if compounding is more than once a year
For continues compounding
Where r = interest rate per period.
N= Number of the compounding period.
m= Number of compounding periods per year.
Effective annual interest rate:
2. Future value of a series of cash flows
Annuity: It is a finite set of fixed payments over a period of time.
An ordinary annuity is an annuity whose payments are made at the end of each period (t = 1)
An annuity-due is an annuity whose payments are made at the beginning of each period. (t = 0)
Future value of annuity
![Fvn = A[((1+r)^N -1) /r]](https://mahesht.com/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_978_6c343a313c87606d3029018af771eb3e.png "Fvn = A[((1+r)^N -1) /r]")
3. Present Value of Single Cash Flow
![Pv = Fv[1/(1+r)^N]](https://mahesht.com/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_971.5_ff84d0959f023a9d77441a8af22fac9b.png "Pv = Fv[1/(1+r)^N]")
which is equivalent to
With Frequency of compounding
4. Present value of series of cash flows
![Pv = A[ (1 - 1/(1+r)^N)/r]](https://mahesht.com/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_982_2a5cfa56920810e27573fdecd34ebc3a.png "Pv = A[ (1 - 1/(1+r)^N)/r]")
which is same as
![Pv = A[ (1 - (1+r)^(- N))/r]](https://mahesht.com/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_982_325edc65d87a571971e14797d994b641.png "Pv = A[ (1 - (1+r)^(- N))/r]")
5. Growth rate which is same as interest rate
