I find it interesting that every paper I do for math involves my stepson Ben but his everyday questions evoke many opportunity to teach (or learn with him).
About two weeks ago my stepson brought me his bankbook and asked why he had such an odd amount of money in his account when he always deposited an even amount of funds (20, 40, etc.). I explained to him that it was the compounded interest accumulated on his account that caused the odd cents. About a half-hour later he approached me again and asked the most insightful question that someone of his age could, ÃÂthen why are there three pennies?ÃÂIt seems that his $1,865.03 bother him because no matter how he tried to figure out where the $.03 (cents) came from he could not. So of course we then sat with pen and calculator in hand and I explained the nature of compound interest.
I told Ben that the compounding of interest involves calculating interest on the sum of his principal and any previous interest that he may have accumulated and that his average interest on his saving account receives the same percentage of interest (approximately 3% a year) but on the already accumulated amount of money. I further explained that he will continue to receive these benefits (more or less, depending if his interest rates change) until he withdrawals his money from the bank.
Then Ben and I worked on an example of what we had just discussed:ASSUMED:LetÃÂs say Ben puts $100.00 in the bank and we will assume the interest is at a rate of 4% annually.
PROBLEM:After one year, Ben checks his account and suddenly he has $104.00. This is because after one year he has collected his interest.
EQUATION FOR YEAR ONE:Future Value is equal to Principal...