Examples of Time Value of Money

Here's a hypothetical example to show how the time value of money works. Let's assume a sum of $10,000 is invested for one year at 10% interest compounded annually. The future value of that money is:

FV=$10,000×(1+10%/1)1×1=$11,000

FV​=$10,000×(1+110%​)1×1=$11,000​

The formula can also be rearranged to find the value of the future sum in present-day dollars. For example, the present-day dollar amount compounded annually at 7% interest that would be worth $5,000 one year from today is:

PV=[$5,000/(1+7%/1)]1×1=$4,673

PV​=[(1+17%​)$5,000​]1×1=$4,673​
 

Would you rather have me give you a dollar today, or a dollar in five years?

A dollar today isn’t worth a dollar in 5 years because of inflation.

Compounding is usually done monthly for some funds, quarterly for stocks and stock funds, and semi-annually for bonds like treasuries and corporates and munis.  A Treasury Bill pays it’s yield at maturity, as do most CDs.  If you’re doing compounding calculations you have to take the different pay schedules into account.

Rule of 72-    Years to double=   72/ Expected rate of return  =  72/10% =7.2

I think it’s useful to demonstrate the danger of inflation.  With inflation at 8%, how long does it take to lose half your money?

 X = 72/8 = 9 Years!    With inflation at a more normal and moderate 3%  x= 72/3 = 24 Years.