Interest Compounding

Interest Compounding

A given principal (A) compounded annually at an interest rate (i) for a given number of years (t) will have a value (V) at the end of that time given by the exponential function

If compounded m times a year for t years,

If compounded continuously at 100 percent interest for one year,

= A(2.71828) = Ae

For interest rates r other than 100 percent and time periods t other than one year,

Effective rate of interest, ie

ie = -1

To find the effective annual rate of interest for continuous compounding:

(1 + ie) =

ie = -1


Discounting is the process of determining the present value (P) of a future sum of money (S). If under annual compounding,

then                                                 A =

Similarly, under multiple compoundings, A = V[1 + (i/m)]-mt and under continuous compounding, .

Discounting a Future Stream of Income