Economic Equivalence 

The values of goods/services at different time points are equivalent due to the time value of money.

Comparison of alternatives on an equivalent basis.

Notations in Equivalence Calculation

P: present worth at time zero

F: future worth at a future time point

A: an end-of-period payment in a uniform series

i: effective interest rate per interest period

N: number of interest periods

Relating P and F of Single Cash Flow

Relating A and F of Uniform Series Cash Flow

Relating A and P of Uniform Series Cash Flow

Linear Gradient Cash Flow

G: an end-of-period payment in a gradient series

Geometric Gradient Cash Flow

f: percentage of payment changes in a geometric series

Special Cases

Varied Interest Rates

Transform cash flows with various interests to P.

Deferred Annuities

The cash flows are deferred to some later periods.

Compounding More Often than Once per Year

Calculating the effective interest rate.

Calculating the actual compounding periods.

Continuous Compounding

Calculate the Effective Interest Rate

Discrete Cash Flows

Single      

                                                        

Uniform Series

                     

Continuous Cash Flows