Math 7 ( Period 4)

Simple Interest 7.8

 Interest is $ paid for the use of money. The amount you deposit or borrow is called the principal. When you put money in a savings account at a bank, the bank pays you interest. When you borrow money from a bank, you must pay the bank interest to the bank in addition to paying bank the money that you borrowed.

The Percent of increase in principal is interest rate. When interest is paid only on the principal you have SIMPLE INTEREST

A principal is an amount borrowed, loaned or saved. An annual interest rate is the percent of the principal you earn or pay as interest for the year. SIMPLE INTEREST is the product of the principal, the annual interest rate,  and the time in years.

Interest = Principal ·rate ·time

I=Prt

Examples:

Example:

 $200 into the bank 6% per year for 1 year.

I = (200) (0.06)(1) = 12

I = (200)(6/100)(1) = 12

I like using fractions if I can simplify before I need to start multiplying

Example:

Deposit $ 500 in savings account for 9 months  simple interest is 1.5%

I = Prt

I = (500)(0.015)(.75)

I = (500)(15/1000)(3/4)

I = $ 5.625 which rounds to $ 5.63

Example:

You borrow $ 250 from your family. After 6 months yu pay back the $ 250 plus $10 in interest. What was the simple interest rate?

I = Prt

What do we know?
10 = (250)(r)(0.5)

10 = 125r

Now we have a simple one step equations

10/125 = r

We still need to put this as a %

simplify 10/125 to

2/25 and that easily changes to 8/100 so the interest rate is 8%

Balance à when you add interest to the principal the result is called the balance.

“A” is used to represent balance

A =  P + I

but then we could write it as

A = P + Prt

Example:
At June 1, a credit card balance was $2500. The cc co charges 21% interest ( annual rate). If no payments are made during  June, what is the balance on July 1?

A = P + Prt

A = 2500 + (2500)(.21)(1/12)  or A = 2500 + (2500)(21/100)(1/12)

A = 2500 + 43.75

A = $2543.75

Some additional examples:

You borrow $1500 from a friend for the down payment on a car. Your friend charges you an annual interest rate of 8% ( Nice friend!) Find the simple interest you will pay in 1 year.

Solution:
Remember   I = Prt

What do you know?

I = (1500) (0.08)(1) 
Most of the time change the interest rate to a decimal. Occasionally you will want to use fractions

Carefully multiply... and

I = 120

Therefore: The simple interest you will pay in 1 year is $120.

You deposit $300 in a savings account. The annual interest rate is 3% ( not much) Find the simple interest you will earn in 1 month.

What do you know?   You know the principal  ( or P in the formula) is $300. You know the annual interest rate ( or r in the formula)  is 3%  But.. wait… be careful…the time must be in years  this is only for one month. The time ( or t in the formula is 1/12)

Solution:

Remember   I = Prt

I = (300)(0.03)(1/12)

I would carefully simplify before I multiplied

I = 0.75

Again, think what does that mean? The simple interest you would earn on $300 in 1 month at that rate is $0.75 When you know the values of any three of the variables in the formula   I = Prt  you can use substitution to find the value of the fourth variable.

Your savings account earns $68 in simple interest in 1 year. The annual interest rate is 8% what is the principal?

Ask yourself, what do I know? What are the three variables  in the formula  I = Prt   that I do know?

$68 is the interest. The rate is 8% and it’s only for 1 year.

so

Remember   I = Prt

68 =P(0.08)(1)

68=0.08p

Solve this one-step equation

Divide both sides by 0.08 carefully

68/0.08 = 0.08p/0.08

850 = p

the principal is $850

You want to open an account with $100.
At Bank A you will earn $0.65 in 3 months.
At Bank B you will earn $2.25 in one year. At which bank will you open your account?
(Although banks do not pay simple interest – they use compound interest, we will assume that Bank A and B are paying only simple interest)

Figure out each bank’s simple interest rate.

Remember   I = Prt  

Bank A:   3 months is 3/12 or ¼  of a year so 

0.65 =  (100)(r) (¼)
0.65= 25r

Solve this one step equation
Divide both sides by 25

0.65/25= 25r/25

0.026= r
We need to change the decimal into a percent
That means Bank A’s rate is 2.6%

Bank B: Yes you can use the formula but look at what you know

2.25 =(100)(r)(1)
That means  r= 0.225
or that the rate for Bank B is 2.25%

You would earn more money if you deposit your savings into Bank A