# Lecture by lonyoo

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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
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
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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