Simple Interest

Section 5.1

Short term loans or investments use simple interest computed at percent-per-year of the principal.

        I = Prt

Future Value is Principal and Interest combined.

        FV = P + I = P + Prt = P(1 + rt)

Businesses use this type of loan for seasonal or inventory equipment, operating costs or tax payments.

Exercise1:  

Borrow $120,000 for 6 months @ 7.9% interest rate.  What is owed at the end of 6 months?  (Hint: convert to years) 

        P = $120,000             r = .079            t = .5year

        I = ($120,000)(.079)(.5) = $4740

        Total owed = FV = $120,000 + $4740 = $124,740

Note: Variables that represent money are: P, FV, I

Variables that are not money: r, t.

This book uses 365 days/ year.

Exercise2:  

How much must be invested now @ 6.2% so that we will have $5000 in 4 years?

        FV = $5000   r = .062           t= 4years   Find P

        $5000 = P[1 + (.062)(4)]

        $5000 
                      =   P   =   $4006.41                                             
        1.248

Add-on Interest: Simple interest charge that is equally distributed over each payment.  Used at car dealerships, furniture stores and types of financing with equal payments.

Exercise3:  

Buy a car for $14,000.  Down Payment of $3000.  Finance the balance @11% for 4 years.  How much are the monthly payments?

        $14,000 - $3000 = $11,000 Loan amount

        FV = $11,000[1 + (.11)(4)] = $15,840 

Total owed at the end of 4 years.

        $15,840  48 Payments = $330/month

Average daily balance (ADB): amount owed for each day averaged by intervals.

        Average Daily Balance  =  S (Daily Balance)(# of days in each interval)/ Total # of Days

Credit cards use ADB to process their Finance charges:

Exercise 4:  

#33.  From March 1 through March 31 (31 days).

 Pervious balance = $157.14, annual rate = 21%

Given:

                        Mar. 5             Payment                                 $25

                        Mar. 17           Tools                                       $36.12

      ADB = 4($157.14) + 12($132.14) + 15(168.26)  = $152.8432258
                                         31 days

Finance charge is simple interest on ADB

        I = ($152.8432258) (.21)(31/365) = $2.73

Finance charge for the 31 day statement with the described transactions = $2.73

Back to Finance, Geometry and Logic Main Page

Back to the Survey of Math Ideas Home Page

Back to the Math Department Home Page

e-mail Questions and Suggestions