9-106th grade math

Using the Interest Formula

Objective

• To use the simple interest formula to calculate interest and find the total amount earned or charged.

• Why? To understand the concept of interest. This is what credit cards charge to use their services. It is what banks charge to either loan out their money or what you may earn from the bank when placing your money in an account. Interest is usually computed for each year.

California State Standards NS 1.0 : Solve problems involving … percentages.NS 1.4 : Calculate given percentages of quantities. AF 1.1 : Write and solve one-step linear equations

in one variable.AF 1.2: Write and evaluate an algebraic expression for

a given situation, using up to three variables.MR 2.7: Make precise calculations and check the

validity of the results from the context of the problem.

MR 3.2: Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

Vocabulary• Interest – The amount of money paid for the use of money

• May be earned $ (+) or owed $ (-)• Interest formula– I = P·R·T– Interest = Principal · Rate · Time (year)

• Principal– An amount of money borrowed or loaned

• MONEY• Rate of interest– A percent of the principal that determines how much

interest is paid or owed. Usually money borrowed has a higher rate (to pay back) and money earning has a lower rate (to get ‘free $)• %

How to Solve Interest Problems

1) Write out the formula: I = P · R · T

2) Substitute the know information.

3) Solve, as an equation. Remember the T for time must be in years or a fraction of the year. Ex.: 5 mo. = 5/12

Put $200 in the bank to earn interest at a rate of 5.5% per year. How much earning per year?

I = PRTI = $200 · 5.5% · 1I = 200 · 0.055 · 1I = $11Total earned per year =

$211

How to Solve Interest Problems

Write out the formula: I = P · R · T

2) Substitute the know information.

3) Solve, as an equation. Remember the T for time must be in years or a fraction of the year. Ex.: 5 mo. = 5/12

P = 3500R = 19%T = 4 mo.I = 3500 · 0.19 · 4/12I = 665 · 1/3 I = $221.67Total paid = 3500 + 221.67= $3721.67

Try It!Complete the tablePrincipal Yearly

rate of int.

Time Interest Total with interest

$6000 5% 5 mo.

$4500 18% 6 mo.

$500 7.5% 1 yr.

Principal Yearly rate Time Interest Total w/interest

$6000 0.05 5/12 $125 $6125

$4500 0.18 6/12 $405 $4905

$500 0.075 1 $37.50 $537.50

Try One More!

4) Borrow $500 for 6 months at 12%. How much will owe bank?

4) I = PRTI = 500 · 0.12 · 6/12I = $30Total owed will be $530

Objective Review • To use the simple interest

formula to calculate interest and find the total amount earned or charged.

• Why? You now understand the concept of interest. This is what credit cards charge to use their services. It is what banks charge to either loan out their money or what you may earn from the bank when placing your money in an account.

• Interest is usually computed for each year.• Simple interest can be found by finding the product of

the principal, the interest rate, and the number of years (if not in year, convert to fraction n/12). To find the total amount, add the interest to the principal.

Independent Practice

• Complete problems 5-10

• Copy original problem first.

• Show all work!

• If time, complete Mixed Review: 11-13

• If still more time, work on Accelerated Math.