If a person has a regular investment plan strategy and interest is paid on the principal, then the accumulation is affected by the amount invested and the interest earned. Interest added to the principal earns interest on the added amounts in subsequent time periods and is called

compounded interest.## TWO MYTHICAL CASES

John and Jack began their professional careers at the same time in 1980.

Jack is a free spirit and said "I am young and want to have a good time. I will wait until later to begin saving for my old age."

John was already worrying about his old age and said, "I will set aside $10,000 per year for my old age."

So, they began their careers, John setting aside $10,000 per year, and Jack having a good time but investing nothing. At the end of 10 years each was over 30 and more mature. John had a nice nest egg of $100,000 plus earned interest. Jack began to realize that he needed to plan for his old age. John on the other hand, began to recognize that he was a workaholic and not enjoying it.

So, after 10 years they each changed their savings strategy. John said, "I will leave my nest egg in place and just let it accumulate interest. I will spend the $10,000 I have been saving on things I would like to do."

Jack, on the other hand, said "I have had my fun and need to be serious about saving for my old age. I will begin investing $10,000 per year and whatever interest is earned.

Compare the growth of the two investment strategies over a period of 30 years.

Prepare an Excel worksheet and graphs. See example graph. A scatterplot may be more appropriate than a line graph. Click here for one example of an Excel worksheet. Prepare your own, it will probably be better.

John will have put in a total of $100,000. Jack will have put in a total of $200,000.

What are some other observations? When will Jack have more money in his nest egg?

What if the delay between strategies was 15 years rather than 10? (

Jack will.)nevercatch upWhat if the delay between strategies was 15 years, but Jack began saving $15,000 per year at that time? (

Jack will "catch up" after 42 years but he will have put it $405,000 whereas John put in $150,000.)Would the contrasts be different if the interest rate was lower? higher?

Adept use of a spreadsheet program can allow for a lot of variation and exploration of this over-simplified idea of exponential growth. Practice some of these explorations with your own spreadsheet. The use of graphs or scatterplots is instructive.