The most common type of loan available to a consumer is a credit card. A credit card allows a consumer to borrow money to pay for things. The card comes with a limit which the borrower can not borrow more than. Interest is charged on what is borrowed in several different. The interest charged is called a finance charge.
Lotus Head from Johannesburg, Gauteng, South Africa [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0/)]
Our goals for this section are to
Compute payments for an add-on loan.
Compute finance charges on a credit card using the unpaid balance method.
Compute the average daily balance to determine credit card charges.
Use the workbook below to help you accomplish these objectives.
Interest is a payment from a borrower to a lender or from a bank to a depositor to compensate them for the use of money. You might take out a loan to finance a purchase and pay the borrower money for the privilege of using the money for some amount of time. You might also deposit money in a bank or credit union and be paid interest on your deposit. The bank will use your money for other purposes such as financing loans to customers and pay you the interest for the use of the money.
How much interest you pay or earn depends on the rate at which you interest is accrued, how much money is being used, and the length of time the money is being used. In addition, interest may be earned or paid as simple interest or compound interest. In this section you will learn how to compute each type of interest.
We have several objectives in this section.
Compute future value using simple interest.
Compute future value using compound interest.
Explain the difference between simple interest and compound interest.
Solve the compound interest formula for different unknowns, such as present value, length, and interest rate of a loan.
Use the workbook and videos below to help you accomplish these objectives.
Caution: The videos below use P0 for the present value or original amount instead of P, You will also find that they use A instead of F for future value.
Be careful in using the compound interest formula…what we call the interest rate per period, the video calls r/m. And the number of compounding periods (the power) they write as nt. All of this is included when we use
where F is the future value, P is the present value, i is the interest rate per period and n is the number of total compounding periods.
Percent is a concept that arises in many areas of daily life. In Chapter 4, we used percent in describing change in exponential equations. In this section, we’ll look at other ways that percents are used to describe portions of amounts (like 84.4% of all children are vaccinated against diphtheria, tetanus and pertussis) and how we can calculate the percent change in a quantity.
Our objectives are
To perform percent calculations.
To compute percent change from data.
To solve applied problems using percents.
Use the workbook and videos below to help you accomplish these objectives.
You might hear a person on the news talking about how some quantity is growing very rapidly. They might describe an epidemic as growing “exponentially”. Or the acres burned in a forest fire as growing “exponentially”. In these contexts, the term “exponential” is used to describe very rapid growth.
Glacier National Park Fire (NPS)
In mathematics, the term exponential can describe growth or decay. It might be rapid or not so rapid. The more important concept is that the change in the quantity occurs at a constant percent rate. If your bank account grows by 2% each year, it is growing exponentially. If the population of a country decreases by 1% each year, it is decaying exponentially.
In this section, our objectives are to
Explain the differences among linear, quadratic, and exponential growth and decay.
Use exponential equations to model growth and decay.
Solve exponential equations using logarithms.
Use the workbook and videos below to help master these objectives.
When a quantity increases or decreases at a constant rate, a linear model like those in Section 4.2 is appropriate. The graph of a linear model is a line and often you may decide to use a linear model if you think a straight line might be useful.
If a quantity is increasing and then changes to decreasing (or vice versa), a linear model will be a poor choice to model the quantity. In this case, a parabola will be a better choice.
Parabolas are equations that have the form
y = a x2 + b x + c
where a, b, and c are numbers (with a ≠ 0). Models that utilize this equation are called quadratic models.
Our objectives in this section are
To use the quadratic formula to solve quadratic equations.
To graph a quadratic equation using the vertex and intercepts.
To use a quadratic equation to model data.
Use the workbook and videos below to help you accomplish these objectives.
