Math 110

Credit Cards. Suppose you got yourself a credit card through the bank: $2000 credit limit 13.6% APR compounded continuously Minimum monthly payment: $43 And… you maxed it out. Dang. If you paid the minimum payment on your card each month, how long would it take you to get rid of your debt?

A P R  Annual Percentage Rate  How much interest you are charged on your balance Let’s talk about interest for a second…

Simple Interest  How do you calculate it? Finds a percentage of your initial amount (principal) and adds it continuously to your total. If I put $50 in an account with a simple monthly interest rate of 8%, how much money would I have at the end of the year? $98 How did you figure it out?

Two types of interest: Lets look at the next kind…  Simple Interest A: amount you end with P: Principle (what you start with) r: interest rate (rate at which it’s growing) t: time (in years usually) A = P (1+ r t)

Compound Interest  How do you calculate THAT?  You are charged a certain amount of interest, it’s added to your balance, then the next time you are charged interest, it’s based off your NEW BALANCE. So….lets say you put $1500 in the bank and has an interest rate of 9% compounded annually. How much will I have in 5 years? 10 years? Answer: $ What about in 10 years if I compounded it quarterly? Answer: $ What about in 10 years if I compounded it monthly? Answer: $

Two types of interest:  Simple Interest A: amount you end with P: Principle (what you start with) r: interest rate (rate at which it’s growing) t: time (in years usually)  Compound Interest A: amount you end with P: Principle (what you start with) r: interest rate (rate at which it’s growing) n: number of compounds per year t: time (in years) A = P (1+ r t)

Keep compounding…  What if you compounded every week?  Every day?  Every hour?  Every minute? Second? Moment? Continuous Compounding:

Now……. What about that credit card you got?

You’ve maxed the sucker out…  $2000  13.6% APR  Compounded continuously! How long IS that gonna take? Lets go to anner/debtplanner.jsp anner/debtplanner.jsp

Statistics on Credit Card Debt  PORT CHARLOTTE, FL (May 31, 2007) According to a new survey released today by CardTrak.com, the median amount of credit card debt carried by Americans is about $6,600 while the mean (or average) credit card debt load is nearly $9,900.

Statistics on Credit Card Debt  Based on an online poll of slightly more than 55,000 consumers that concluded in April, 61% said they carryover debt each month on their credit cards, while 31% said they pay-off balances monthly and 7% stated they have no credit cards.

Statistics on Credit Card Debt  Of cardholders carrying debt, over 64% had balances under $10,000. However, an astonishing 13% of the same group said they carry total credit card balances in excess of $25,000.

Statistics on Credit Card Debt  At the end of 2006, Americans owed $745 billion on general purpose credit cards including $641 billion on VISA®/MasterCard® cards, and $104 billion on American Express®/Discover® cards, according to CardWeb.com ( Consumers also owed an estimated $105 billion on limited purpose cards or store/gas credit cards. In total, American cardholders owed $850 billion on all credit cards as of December 31, 2006, according to CardWeb.com (

Things to remember… "Remember this: debt is a form of bondage. It is a financial termite. When we make purchases on credit, they give us only an illusion of prosperity. We think we own things, but the reality is, our things own us…Some debt— such as for a modest home, expenses for education, perhaps for a needed first car— may be necessary. But never should we enter into financial bondage through consumer debt without carefully weighing the costs." (Joseph B. Wirthlin, "Earthly Debts, Heavenly Debts," Ensign, May 2004, 40-41).

" Interest never sleeps nor sickens nor dies; it never goes to the hospital; it works on Sundays and holidays; it never takes a vacation; it never visits nor travels; it takes no pleasure; it is never laid off work nor discharged from employment; it never works on reduced hours; it never has short crops nor droughts; it never pays taxes; it buys no food; it wears no clothes; it is unhoused and without home and so has no repairs, no replacements, no shingling, plumbing, painting, or white- washing; it has neither wife, children, father, mother, nor kinfolk to watch over and care for; it has no expense of living; it has neither weddings nor births nor deaths; it has no love, no sympathy; it is as hard and soulless as a granite cliff. Once in debt, interest is your companion every minute of the day and night; you cannot shun it or slip away from it; you cannot dismiss it; it yields neither to entreaties, demands, or orders; and whenever you get in its way or cross its course or fail to meet its demands, it crushes you." (J. Reuben Clark Jr., in Conference Report, Apr. 1938, 103).

Continuous Exponential Growth  I possess a colony of bacteria on a petri dish with agar (and agar tastes nasty): If the number of bacteria doubles in 3 hours, find the formula that could tell me how many bacteria I have at any given time. How long would it take for my colony to triple? How long would it take the population to get ten times as big as it was to start with?