Simple and Compound Interest

1 8 Simple and CompoundInterestInterest is the fee paid for borrowed money. We receiveinterest when we let others use our money (for example, bydepositing money in a savings account or making a loan).We payinterest when we use other people s money (suchas when we borrow from a bank or a friend). Are you a receiver or a payer ?In this chapter we will study Simple and compoundinterest. Simple interestis Interest that is calculated onthe balance owed but not on previous Interest . Compoundinterest, on the other hand, is Interest calculated on anybalance owed including previous Interest .

2 Interest for loansis generally calculated using Simple Interest , while interestfor savings accounts is generally calculated using com-pound concepts of this chapter are used in many upcom-ing topics of the text. So hopefully you have interestin mas-tering the stuff in this Computing Simple Interest andmaturity value aComputing Simple Interest and maturity value loans stated in months or years bCounting days and determining maturity date loans stated in days cComputing Simple Interest loans stated in daysUnit Solving for principal, rate, and time aSolving for P(principal) and T(time) bSolving for R(rate)

3 Unit Compound Interest aUnderstanding how Compound Interest differs fromsimple Interest bComputing Compound Interest for different com-pounding periods151On July 10, 2005, Wendy Chapman borrowed $12,000 from her Aunt Nelda. If Wendy agreed topay a 9% annual rate of Interest , calculate the dollar amount of Interest she must pay if the loan isfor(a) 1 year, (b)5 months, and (c)15 year:I= PRT= $12,000 9% 1 = $1, months:I= PRT= $12,000 9% 5 12= $ months:I= PRT= $12,000 9% 1512= $1,350We can do the arithmetic of Example 1 with a calculator:what is PRT?

4 152 Chapter 8 Simple and Compound InterestUnit Computing Simple Interest and maturity valueWendy Chapman just graduated from college witha degree in accounting and decided to open herown accounting office (she can finally start earningmoney instead of paying it on college). On July 10,2005, Wendy borrowed $12,000 from her AuntNelda for office furniture and other start-up agreed to repay Aunt Nelda in 1 year, togetherwith Interest at 9%.The original amount Wendy borrowed $12,000 is the principal. The percent thatWendy pays for the use of the money 9% is therate of Interest (or simply the Interest rate).

5 Thelength of time 1 year is called the timeorterm. The date on which the loan is to be repaid July 10, 2006 is called the due dateor maturitydate. The total amount Wendy must repay (whichwe will calculate later) consists of principal($12,000) and Interest ($1,080); the total amount($13,080) is called the maturity value. aComputing Simple Interest and maturity value loans stated in months or yearsTo calculate Interest , we first multiply the principal by the annual rate of Interest ; this gives us inter-est per year. We then multiply the result by time (in years).

6 Example 1 Remember, when symbols are written side by side, it means to multiply, so PRTmeans P R T. Also,don t forget R, the Interest rate, is the annualrate; and Tis expressed in years(or a fraction of a year).TIPI= PRTI= Dollar amount of Interest P= Principal R= Annual rate of Interest T= Time (in years) Simple Interest formula=Banks provide a valuable service as money bro-kers. They borrow from some people (throughsavings accounts, etc.) and loan that samemoney to others (at a higher rate). Some ofthese loans are Simple Interest (for most calculators)12,000 9% =1, ,000 9% 5 12= ,000 9% 15 12=1, to Example 1.

7 Calculate the maturity value if the 9% $12,000 loan is for (a)1 year, (b)5months, and (c)15 year:M= P+ I= $12,000 + $1,080 = $13, months:M= P+ I= $12,000 + $450 = $12, months:M= P+ I= $12,000 + $1,350 = $13,350 Wendy must pay a total of $13,080 if the loan is repaid in 1 year (July 10, 2006), $12,450 if the loanis repaid in 5 months (December 10, 2005), and $13,350 if the loan is repaid in 15 months (October10, 2006).Unit Computing Simple Interest and maturity value153 Example 2To find the maturity value, we simply add Interest to the P+ IM= Maturity value P= Principal I= Dollar amount of interestmaturity value formula= bCounting days and determining maturity date loans stated in daysIn Examples 1 and 2, the term was stated in months or years.

8 Short-term bank loans often have aterm stated in days (such as 90 or 180 days) rather than months. Before calculating the amount ofinterest for these loans, we must know how to count days. One method is to look at a regular calen-dar and start counting: the day afterthe date of the loan is day 1, and so on. However, that methodcan be time-consuming and it is easy to make a mistake along the way. We will, instead, use a day-of-the-year calendar, shown as Appendix D; pay special attention to the entertaining footnote. In theday-of-the-year calendar, each day is numbered; for example, July 10 is day 191 (it is the 191st dayof the year).

9 The next example shows how to use a day-of-the-year (a)90 days from September 10, 2006;(b)180 days from September 10, 2006; and (c) 180days from September 10, 10 Day253+90 Dec. 9 10 Day253+180433(This is greater than 365, so we must subtract 365)-365 Mar. 9 10 Day253+180433(This is greater than 365, so we must subtract 365)-365 Mar. 8 68(Because this is a leap year, March 8 is day 68)In parts (b) and (c) of Example 3, we found that the final date was the 68th day of the year. Fora non-leap year, the 68th day is March 9. With a leap year, like 2008, there is an extra day in Februaryso March 9 is day 69; March 8 is day number optional method for counting days is known as the days-in-a-month method.

10 With thismethod, we remember how many days there are in each month; the method is shown in AppendixD, page D-2. While a day-of-the-year calendar is often easier to use, understanding the days-in-a-month method is important because we may not always have a day-of-the-year calendar with is how we could do Example 3, part (c), using the days-in-a-month method:Example 3154 Chapter 8 Simple and Compound InterestIn the next example, we ll figure out how many days between two dates. For some of us, thereare quite a few days between dates (oops, wrong kind of date).