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Good morning! Here is today's warm-up problem: A family buys a home, borrowing $170,000 with a mortgage that requires them to pay $1,020 per month for 30 years. (a) What is the total amount they pay the bank over the entire 30 years? (b) How much of that is interest (as opposed to paying back the $170,000)? Exploration: Credit Card Math Imagine that you have a $200 credit card debt this month. This is the balance on your card. To avoid a fee, your card requires you to pay at least 2% of your credit card balance each month as a minimum payment. What is your minimum payment this month? Exploration: Credit Card Math So your balance is $200, and your minimum payment is $4. This credit card has an interest rate of 15%. This is an annual interest rate. (Almost every interest rate is described as a annual amount.) To find the monthly interest rate we need to divide the 15% by 12. What is the monthly rate, expressed as a percent and as a decimal? Exploration: Credit Card Math So your balance is $200, your minimum payment is $4, and the monthly interest rate is 1.25% (or 0.0125). What is the interest you must pay this month on your $200 balance? If you paid the minimum payment of $4, how much would be left over to pay off some credit card debt? Lecture: Credit Card Math All credit card problems work the same way. Make a table that looks like this: Payment Interest Balance Min. Actual As % As $ Paid Off Lecture: Credit Card Math For each month, fill out a row of the table. Payment Interest Balance Min. Actual Monthly % As $ Paid Off $200 ×.02=$4 $4 0.0125 $2.50 $1.50 $198.50 In the homework we will assume you have stopped spending money, so each month's balance is the old one minus what you pay off. Lecture: Credit Card Math Now you can see why it is best to pay more than the minimum payment on a credit card. This person decided to pay 10 times the minimum payment. Much more than 10 times is paid off! Payment Interest Balance Min. Actual Monthly % As $ Paid Off $200 ×.02=$4 $40 0.0125 $2.50 $37.50 $198.50 Lecture: Credit Card Math Payment Interest Balance Min. Actual Monthly % As $ Paid Off $200 ×.02=$4 $40 0.0125 $2.50 $37.50 $198.50 $37.50 is what percent of $1.50? Ten times $1.50 would be what % of $1.50? Lecture: Credit Card Math Time to do a problem! Let's do § 6.8 #1. Work as much as you can by yourself, then we will go over the work together. Payment Interest Balance Min. Actual Monthly % As $ Paid Off $4,876.54 Lecture: Credit Card Math In § 6.8 there are also problems about debt from student loans or mortgages. These are exactly the same, except that the loan company tells you how much to pay each month and it does not change. So skip the step where you calculate the minimum payment. The actual payment is always a fixed amount provided for you. Lecture: Credit Card Math Unfortunately, seeing how credit card debt changes over time takes a lot of math. We do not want to fill out many rows for these tables! Fortunately, we can make a spreadsheet do the work for us. Watch my example, and then if you wish we can go to the computer lab and all do this together.
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