Estimating Probability Distribution for the Random Time Variable in the Continuous Compounding Formula: Implication to Time Value of Money in Investment Decisions

Abstract

This paper treats the time “t” variable in the continuous compounding formula of the time value of money as a random variable and derives a probability distribution for it. It formulates a mathematical model that shows the probability associated with the time of recouping the present value of the investment at a specified time and estimates the time at which a given asset changes, holding other factors constant. The study finds that there is an indirect relationship between the investment holding period and the probability of obtaining an investment return on the future value of an asset. It also finds that there is a maximum threshold of time that maintains the present value of an asset after which the probability decreases. This paper differs from previous studies by modeling time as a random variable.