Borrowing and lending are two sides of the same transaction. The amount borrowed/loaned is called the principal. To the borrower, the principal is a debt; to the lender, the principal represents an investment. The interest paid by the borrower is the lender's investment income. There are two systems1 for calculating interest. * Simple interest is a system whereby interest is calculated and paid only on the principal amount. Simple interest is used mainly for short-term loans and investments. (By “short-term” we mean durations of up to one year.) Chapters 6 and 7 cover the mathematics and applications of simple interest. * Compound interest is a system whereby interest is calculated and added to the original principal amount at regular intervals of time. For subsequent periods, interest is calculated on the combination of the original principal and the accumulated (or accrued) interest from previous periods. Compound interest is used mainly (but not exclusively) for loans and investments with durations longer than one year. Chapters 8 and beyond cover the mathematics and applications of compound interest. The rate of interest is the amount of interest (expressed as a percentage of the principal) charged per period. Simple interest rates are usually calculated and quoted for a one-year period. Such a rate is often called a per annum rate. That is,

Note: If a time interval (such as “per month”) is not indicated for a quoted interest rate, assume the rate is an annual or per annum rate. The rate of interest charged on a loan is the lender's rate of return on investment. (It seems more natural for us to take the borrower's point of view because we usually become borrowers before we become lenders.) If you “go with your intuition,” you will probably correctly calculate the amount of simple interest. For example, how much interest will $1000 earn in six months if it earns an 8% rate of interest? Your thinking probably goes as follows: “In one year, $1000 will earn $80 (8% of $1000). In six months ( year), $1000 will earn only $40 ( of $80).” Now write an equation for the preceding calculation, but in terms of the following symbols: * I = Amount of interest paid or received

* P = Principal amount of the loan or investment

* r = Annual rate of simple interest

* t = Time period (term), in years, of the loan or investment To obtain the $40 (I) amount, you multiplied $1000 (P) by 0.08 (r) and by year (t). In general,

TIP Interest Rates in Algebraic Formulas

When substituting the numerical value for an interest rate into any equation or formula, you must use the decimal equivalent of the interest rate. For example, 9% would be expressed as 0.09 in an equation. Page 184

TIP Avoid “Formula Clutter”

Don't try to memorize other versions of formula (6-1) that have different variables isolated on the left-hand side. In any problem requiring formula (6-1), just substitute the three known variables and then solve for the remaining unknown variable. EXAMPLE 6.1A CALCULATING THE AMOUNT OF INTEREST

What amount of interest will be charged on $6500 borrowed for five months at a simple interest rate of 11%? SOLUTION

Given:

Since no time period is given for the 11% rate, we understand that the rate is per year. The amount of interest payable at the end of the loan period is

Check your understanding: Redo the question, this time assuming the money is borrowed for eight months. (Answer: I = $476.67) Related problem: #1 on page 186

EXAMPLE 6.1B CALCULATING THE PRINCIPAL AMOUNT

If a three-month term deposit at a bank pays a simple interest rate of 4.5%, how much will have to be deposited to earn $100 of interest? SOLUTION

Given: year, r = 4.5%, I = $100. Substitute these values into I = Prt.

Check your understanding: Redo the question, this time using a simple interest rate of 3.75%. (Answer: $10,666.67 must be deposited) Related problem: #7 on page 186

EXAMPLE 6.1C CALCULATING THE...