Simple & Compound Interest 7-8
When you first deposit money into a bank or savings & loan, your money is called principal.
The bank takes you money and invests it. In return, the bank pays you interest– currently NOT MUCH– based on the interest rate.
Simple interest is interest paid ONLY on the principal.
Simple Interest Formula (yes, you need to memorize this formula)
I = PRT
Where I = Interest
P = the principal ($$ in savings or $$ owed to creditors)
R= interest rate PER YEAR (this is a % you must change to a decimal or fraction)
T = the time IN YEARS ( so if you have 9 months you really have 9/12 of a year)
Suppose you deposit $400 in a saving account. The interest rate is 5% per year.
(a) Find the interest earned in six years. Find the total of principal PLUS interest.
What’s the formula?
I = PRT
What parts of the formula do we know?
PLUG THEM IN
I = (400)(.05)(6)
Solve for I
Interest = $120.00 Now what is left to do?
(b) Find the interest earned in 3 months. Find the total of principal PLUS interest
What’s the formula?
I = PRT
What parts of the formula do we know? PLUG THEM IN
I = (400)(.05)(.25)
Solve for I
Interest = $5.00 Now what is left to do?
You just bought an ipod for $300 on your parent’s credit card (and you promised to pay them back– (“really, Mom”) in 2 years. Your parents are charging you the rate on their credit card, which is
20% interest.
How much interest will you pay and what is the total you will have to pay your parents so they can pay VISA?
What’s the formula?
I = PRT and what information do we have?
Plug it in, plug it in… plug it in….. I =300(.20)(2)
I = $120.00
How much will VISA get on your purchase?
Compound Interest is very similar to simple but you get
charged INTEREST on the INTEREST . So…
COMPOUND > SIMPLE
always
The ipod you bought and are paying over two years on the VISA but this time interest is COMPOUNDED (added to the principal)
ANNUALLY ( each year)
After one year I = ($300)(.20)(1) = $60
$300 Ipod + $60 interest = $360
Now in year 2, you are charged interest on the
$360 ( not the originally $300)
Now in year 2, you are charged interest on the
$360 ( not the originally $300)
Year 2: ( $360)(.20)(1) = $72
$360 owed at the end of year 1 + $72 = $432 owed at the end of year 2.
Remember simple interest was $ 420.
Interest can be compounded
annually ( once a year),
semiannually ( twice a year),
quarterly ( 4 times a year),
monthly ( 12 times a year), or even
daily ( 365 times a year)
Which would give you the most interest on your savings deposit?
Which would give the VISA company the most?
Guess what they use… DAILY
There is a formula for compound interest:
Balance owed =
principal (1 + percent rate[time])number of compoundings
So if I owe VISA $500 at 6% compounded quarterly( 4 times a year) and I want to know how much I will owe after 1 year.. I can use this formula: A = P(1 + rt)n
A is the amount I am looking for
P = $500 r = 6% or 0.06 t = ¼ of a year or .25
n = 4 because I want to know after a year and the interest will be compounded 4 times
A = 500[1 + (.06)(.25)]4 where is that calculator
A = 500(1.015)4
A = 500 (1.06136)
A = $530.68 rounded to the nearest cent at this point.
The other way is to organize a table and calculate the interest each time 500(.06)(.25) = 7.50 interest 1st quarter
500 + 7.50 = $507.50
507.50(.06)(.25) = $7.61 interest 2nd quarter
507.50 + 7.61 = $515.11
515.11(.06)(.25) = $ 7.73 interest 3rd quarter
$515.11 + 7.73 = $ 522.84
522.84(.06)(.25) = $7.84 interest 4th quarter
$522.84 + 7.84 = $ 530.68
You wouldn’t want to use the table approach more than one year because it just takes too much time!!
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