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
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