Financial math: can time be negative?

The tutor answers a question that brought someone to his site.

These days, Oracle Tutoring gets between 5000 and 6000 distinct visitors per month. Looking over the raw log entries of how some visitors arrived, I saw an inquiry yesterday that I’m sad to say may have gone unsatisfied. The literal query:

financial math can time be negative?

It’s a great question, but I don’t think I’ve covered it specifically – until now. In honour of that brave inquirer, here’s my response:

Let’s consider the compound interest formula



A=accumulated amount after time t

P=principal amount (amount today)

i=annual interest rate

t=time in years

In this context, negative t can represent years previous.

Example 1: Using negative time, find the amount that would have been invested three years ago, at 3.2% compounded annually, to be worth 5000 today.

Solution: In this case, A will represent the amount needed back then to give 5000 now; P will be 5000, the amount today. The interest rate 3.2% must be written in decimal form 0.032:


Entering the expression straight into a forward-entry calculator gives


Using negative time, we have back-valued today’s principal of 5000 to what it would have been, in that account, three years ago.

I love raw, straightforward questions like that. HTH:)


Tan, Soo Tang. Applied Finite Mathematics. Boston: PWS-KENT, 1990.

Thanks to

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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