# Lesson #1: The Time Value of Money

The first lesson in finance is the time value of money. The concept behind this is that a person would prefer a dollar today as opposed to a dollar in the future. Ignore for purposes of this discussion, inflationary effects and currency related issues. They can be factored in later.

If you have \$1.00 today and can put it to work through an investment for a given period (say 1 year) and get \$0.05 in profit without losing any part of my dollar, you would have made a 5% profit. If it is a sure thing, You should would not lend that dollar out for that year for anything less than receiving \$1.05 at the end of the year.

The above is a relationship between the interest rate for a given period (usually in years), and a principal amount; the \$1.00 in this case.

Using the following variables, a formula can be established:

i= interest rate, t= time, P= present value (the principal), F= future value

F=P*(1+i)^t the time rate of money basic equation

We’ll try this equation for a more complex situation:

“I invest \$1000 for a period of 7 years in a long-term CD at an annual interest rate of 3.5%. What will my future value be?”

The first step is to establish our variables:

i=3.5%, t=7, P=1000, F=unsolved

F=1000*(1.035)^7=\$1272.28

A gain of \$272.28 over the 7 years.

This equation can be re-worked to solve for any one of the four variables. For example:

P=F/[(1+i)^t]

t=[ln(F/P)]/[ln(1+i)] This one’s a bit more complex. The “ln” function is the natural log function.

For some fun, try solving for i.

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