Lesson 7-7 Simple and Compound Interest
Interest (I) – the amount of money paid or earned for the use of money.
Simple Interest – paid only on the initial principal of a savings account or loan.
Principal (P) – the initial amount of money put into an account or borrowed
Rate (r) – annual interest rate as a decimal
Time (t) – time in years
I=Prt
Example 1 Find Simple Interest
a. Find the simple interest for $600 invested at 5% for 4 years.
I = prt
Write the simple interest formula.
I = 600  0.05  4
Replace p with 600, r with 0.05, and t with 4.
I = 120
Simplify.
The simple interest is $120.
b.
Find the simple interest for $3200 invested at 7.5% for 2 years.
I = prt
Write the simple interest formula.
I = 3200  0.075  2 Replace p with 3200, r with 0.075, and t with 2.
I = 480
Simplify.
The simple interest is $480.
Example 2 Find the Interest Rate
INVESTING Suppose Patrick placed $3500 in the bank for 3 years. He earns
$25.80 in interest each month. Find the annual interest rate.
Understand You need to find the simple interest rate.
Plan
Use the formula I = prt.
Solve
First, find the total amount of interest he will earn.
$25.80  36 = $928.80
Multiply to find the total amount;
3 years = 36 months.
So, I = $928.80.
The principal is $3500. So, p = 3500.
The time is 3 years. So, t = 3.
I = prt
928.80 = 3500  r  3
928.80 = 10,500r
928.80 10,500r
=
10,500 10,500
0.0885  r
Write the simple interest formula.
Replace I with 928.80, p with 3500, and t with 3.
Simplify.
Divide each side by 10,500.
Simplify.
The simple interest rate is about 0.0885 or 8.85%.
Check
Use the formula I = prt.
$3500  0.0885  3 or $929.25, and $929.25  $928.80. 
Compound Interest – amount of interest paid on the initial principal and on interest
earned.
Example 3 Find the Total Amount
What is the total amount of money in an account where $1800 is invested at an
interest rate of 6.25% compounded annually for 3 years?
STEP 1
Find the amount of money in the account at the end of the first year.
I = prt
Write the simple interest formula.
I = 1800  0.0625  1
Replace p with 1800, r with 0.0625, and t with 1.
I = 112.5
Simplify.
1800 + 112.5 = 1912.50
Add the amount invested and the interest.
At the end of the first year, there is $1912.50 in the account.
STEP 2
Find the amount of money in the account at the end of the second year.
I = prt
Write the simple interest formula.
I = 1912.50  0.0625  1
Replace p with 1912.50, r with 0.0625, and t with 1.
I  119.53
Simplify.
So, the amount in the account after 2 years is about $1912.50 + $119.53 or
$2032.03.
STEP 3
Find the amount of money in the account at the end of the third year.
I = prt
Write the simple interest formula.
I = 2032.03  0.0625  1
Replace p with 1912.50, r with 0.0625, and t with 1.
I  127.00
Simplify.
So, the amount in the account after 3 years is about $2032.03 + $127.00 or
$2159.03.