Math in Our World
Section 8.2
Simple Interest
Warm Up
Multiply.
1. x(x3)
3. 2(5x3)
x4
10x3
5. xy(7x2)
7x3y
6. 3y2(–3y)
–9y3
2. 3x2(x5)
3x7
4. x(6x2)
6x3
Learning Objectives
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Compute simple interest and future value.
Compute principal, rate, or time.
Compute interest using the Banker’s rule.
Compute the true rate for a discounted loan.
3.) Use formulas or equations of functions to
calculate outcomes of exponential growth or
decay. (Alabama)
Interest
Interest (I ) is the fee charged for the use of
money.
Simple interest is a one-time percent of an
amount of money.
Interest
Principal (P) is the amount of money borrowed or
placed into a savings account.
Rate (r) is the percent of the principal paid for having
money loaned, or earned for investing money. Unless
indicated otherwise, rates are given as a percent for a
term of 1 year.
Time (t) or term is the length of time that the money is
being borrowed or invested. When the rate is given as
a percent per year, time has to be written in years.
Future value (A) is the amount of the loan or
investment plus the interest paid or earned.
Interest
Formulas for Computing Simple Interest
and Final Value
1. Interest = principal x rate x time:
I = Prt
2. Future value principal interest:
A = P + I or A = P (1 + rt)
EXAMPLE 1
Computing Simple Interest
Find the simple interest on a loan of $3,600.00 for
3 years at a rate of 8% per year.
SOLUTION
Change the rate to a decimal and substitute into the
formula I = Prt:
8% = 0.08
I = Prt
= ($3,600.00)(0.08)(3)
= $864.00
The interest on the loan is $864.00.
EXAMPLE 2
Finding Future Value
Find the future value for the loan in Example 1.
SOLUTION
Recall that the Principal is $3,600.00 and the Interest on
the loan is $864.00.
Substitute into the formula A = P + I
= $3,600.00 + $864.00
= $4,464.00
The total amount of money to be paid back is $4,464.00.
EXAMPLE 3
Computing Simple Interest for
a Term in Months
To meet payroll during a down period, United
Ceramics Inc. needed to borrow $2,000.00 at 4%
simple interest for 3 months. Find the interest.
SOLUTION
Change 3 months to years by dividing by 12, and change the
rate to a decimal.
Substitute in the formula I = Prt.
EXAMPLE 4
Computing Monthly Payments
Admiral Chauffeur Services borrowed $600.00 at
9% simple interest for 1-1/2 years to repair a
limousine. Find the interest, future value, and the
monthly payment.
SOLUTION
Step 1 Find the interest.
EXAMPLE 4
Computing Monthly Payments
SOLUTION
Step 2 Find the future value of the loan.
Step 3 Divide the future value of the loan by the number of
months. Since 1-1/2 years = 18 months, divide $681.00 by 18
to get $37.83.
The monthly payment is $37.83.
EXAMPLE 5
Computing Principal
Phillips Health and Beauty Spa is replacing one of
its workstations. The interest on a loan secured by
the spa was $93.50. The money was borrowed at
5.5% simple interest for 2 years. Find the principal.
SOLUTION
The amount of the loan was $850.00.
EXAMPLE 6
Computing Interest Rate
R & S Furnace Company invested $15,250.00 for
10 years and received $9,150.00 in simple
interest. What was the rate that the investment
paid?
EXAMPLE 6
Computing Interest Rate
SOLUTION
The interest paid on the investment was 6%.
EXAMPLE 7
Computing the Term of a Loan
Fran and Rick borrowed $4,500.00 at 8-3/4% to
put in a hot tub. They had to pay $2,756.25
interest. Find the term of the loan.
SOLUTION
The term of the loan was 7 years.
The Banker’s Rule
The Banker’s rule treats every month like it has 30
days, so it uses 360 days in a year, instead of 365.
They claim that the computations are easier to do.
When a lending institution uses 360 days instead of
365, how does that affect the amount of interest?
For example, on a $5,000 loan at 8% for 90 days, the
interest would be
EXAMPLE 8
Using the Banker’s Rule
Find the simple interest on a $1,800 loan at 6% for
120 days. Use the Banker’s rule.
SOLUTION
Discounted Loans
Sometimes the interest on a loan is paid
upfront by deducting the amount of the
interest from the amount the bank gives you.
This type of loan is called a discounted loan.
The interest that is deducted from the amount
you receive is called the discount.
EXAMPLE 9
Finding the True Rate of a
Discounted Loan
A student obtained a 2-year $4,000 loan for
college tuition. The rate was 9% simple interest
and the loan was a discounted loan.
(a) Find the discount.
(b) Find the amount of money the student
received.
(c) Find the true interest rate.
EXAMPLE 9
Finding the True Rate of a
Discounted Loan
SOLUTION
(a) The discount is the total interest for the loan.
(b) The student received $4,000 - $720 = $3,280.
EXAMPLE 9
Finding the True Rate of a
Discounted Loan
SOLUTION
(c) The true interest rate is calculated by finding the rate on
a $3,280 loan with $720 interest.
The true interest rate is approximately 10.98%.