One of the most common financial instruments a person will ever encounter is an installment loan such as a car or home loan. For these types of loans, an amount of money is borrowed. This amount plus interest is paid back over with fixed payments. In general, payments are made on a monthly basis. The length of time over which the payments are made (the term) may be as short as 36 to 72 months for an auto loan. Or the payments may be made over a 15 to 30 year term for a home loan.
Since these loans behave like a decreasing annuity, we can use the formulas we have developed in earlier sections to compute the payment on the loan. In this section we will compute the payment for several different loans and track those payments in a special type of table called an amortization table.
A sequence of payments or withdrawals made to or from an account at regular time intervals is called an annuity. The term of the annuity is length of time over which the payments or withdrawals are made. There are several different types of annuities. An annuity whose term is fixed is called an annuity certain. An annuity that begins at a definite date but extends indefinitely is called a perpetuity. If an annuities term is not fixed, it is called a contingent annuity. Annuities that are created to fund a purchase at a later date like some equipment or a college education are called sinking funds.
The payments for an annuity may be made at the beginning or end of the payment period. In an ordinary annuity, the payments are made at the end of the payment period. If the payment is made at the beginning of the payment period, it is called an annuity due. In this text we’ll only examine annuities in which the payment period coincides with the interest conversion period. This type of annuity is called a simple annuity.
Many applications in business are based upon a rate of growth or decay given as a percentage. For instance, the rate at which the value of a $150,000 home is increasing may be given as 2% per year. The value of the home t years later would be
Other quantities will decrease by a percentage. At the completion of a marketing campaign, sales for a new tablet computer are 550,000. Sales decrease by 5 percent per week from that point onward. The sales t weeks later may be modeled by
Each of these quantities are modeled by an exponential function of the form
where a is the original amount of the quantity and r is the rate in percent per time. The time should correspond to the units of time on the variable t. The plus sign is used when the function is an increasing exponential function. The minus sign is used when the quantity is decreasing.
In this section, you’ll learn how to use logarithms to solve equations arising from exponential functions.
Businesses operate with borrowed money. When a business needs order inventory or expand, it may borrow the money needed for the expansion. The borrower will be charged interest for the opportunity to use the money. The interest on the loan is typically charged at some percentage of the amount borrowed called the interest rate.
Not only do businesses borrow, but banks may also borrow money from other banks or even individuals. For instance, you may invest money with a bank and receive interest from the bank. Most consumers borrow money regularly using credit cards. If the balance is not paid off when the lending period is through, you must pay interest to the credit card company for the privilege of borrowing the money.
In this section, we’ll examine several type of interest. Simple interest is interest where a fixed amount is paid based on the amount borrowed and the length of time the money is borrowed. In compound interest, interest accumulates according to the amount borrowed over time and any interest that has accumulated during that period of time. Both types of interest are used extensively in business and finance.
In this chapter you will learn about about interest and how it accrues in various financial applications. We’ll look at simple and compound interest as well as annuities and mortgages. For some of you, it may the first time during the course you say, “Finally, something that might really be useful in business!”
Mr. Satterly [WTFPL]
All of these problems about loans, annuities, and mortgages are clear cut, but come with a dark side…they are nasty long and hard to memorize.
Your main job will be to know what each formula is used for, what the letters represent, and how to solve for the different quantities in an application.
Mastering these formulas will allow you to meet the objectives for this chapter.
Compute quantities involved in simple and compound interest.
Compute quantities involved in annuities and mortgages.
