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

 Transaction Date # of Days Owe Balance Mar. 1-5 4 \$157.14 Payment Mar. 5-17 12 \$132.14 Purchase Mar. 17-31 15 \$168.26

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