Math 6H ( Periods 3, 6, & 7)

Simple Interest 9-7
When you borrow money you pay the lender INTEREST for the use of the money. The amount of interest you pay is usually a percent of the amount borrowed figured on a yearly basis. This percent is called the annual rate.

When interest is computed year by year we call it
SIMPLE INTEREST
The formula is I= Prt

Let I = simple interest charges
P = principal ( amount borrowed)
r= annual rate
t = time in years

I = Prt

simple interest is calculated just on the principal.
Let's work through a few examples

$150 borrowed at 12% annual rate for 1 year

I = Prt

I = (150)(.12)(1)
I = 18
so you would owe $18 in interest after 1 year.
The total due would be $150 + 18 = $168

What if instead you borrowed the same amount but for 2 years... nothing was due until the end of two years
I = Prt
I = 150(.12)(2) = 36
You would owe $36 in interest .. so the total due was 150 + 36 = $ 186.

What if you borrowed the same amount for 3 years...
I = 150(.12)(3) = 54 or $54 in interest.
You would owe 150 + 54 = $ 204 after three years...

However, let's say you could only borrow that amount for 6 months...
I = Prt
I = (150)(.12)(.5)
Why 0.5? that is 1/2 a year.
Now you can always multiply by 1/2 as well.. in fact, sometimes that is easier
I = 150(.12)(1/2) = 9 or $ 9.00

After 6 months you would owe $159.


Dylan paid $375 in interest on a loan of $1500 principal at 12.5% interest.
What was the length of time?

Look at what it is asking and see which of the variables you have...
I= Prt
We have the interest paid, the principal and the annual rate so
375= (1500)(.125)(t)

375 = 187.5t
solve this one step equation by dividing both sides by 187.5

375 = 187.5t
187.5 187.5

t = 2

so 2 years

divide carefully...

Alexis paid $ 585 simple interest on a $6500 loan for 6 months.

what was the annual rate?

What do we know?
I = 585
P = 6500
t= 6 months ( which is 0.5 or 1/2)

I = Prt
585 = 6500 (r)(.5)
585 = 3250r
divide both sides by 3250

585 = 3250r
3250 3250

r = 0.18
which means 18%



annual--> once a year
6 months --> 1/2 or 0.5
4 months--> 1/3
3 months --> 1/4 or 0.25
8 month --> 2/3


Compound Interest 9-8

Compound interest is ALWAYS more than simple interest.

interest is compounded on the interest!!

$100 savings earning $10 interest/ annual.. [this only happens NOW if your dad is the one paying you... :)]

I = Prt
at the end of the first year
I = 100(.10)(1) = 10 or $10
add that to the 100
$110.
Now for the 2nd year,
$110 is your principal
so
I = Prt
I = 110(.10)(1) = 11 or $11
so at the end of 2 years you have $110 + 11 or $121

Now for the 3rd year
I = Prt
I = 121(10)(1) = $12.10
So at the end of three years you have $121 + 12.10 = $133.10

What if you had $500 at 8% compounded quarterly for one year.

quarterly means 1/4 or .25

I = Prt
I = 500(.08) (1/4)
calculate the 08(1/4) because that will be the constant you will multiply your principal by each time
(.08)(1/4) = .02
so I = 500(.02) = 10
after the first quarter it is 510
I = Prt for the 2nd quarter
I = 510 (.02) = 10.20
so after the 2nd quarter $510 + 10.20 = $520.20
I = Prt for the third quarter
I = 520.20 (0.02) = about $10.40 ( round to the nearest penny)
so after the third quarter
$520.20 + 10.40 = $530.60
I = Prt
I = 530.60(.02) = about $10.61
So at the end of 4 quarters -- or one year
530.60 + 10.61 = $541.21

compounding terms:
annually--> once a year
semiannually --> twice a year
quarterly--> four times a year
monthly--> 12 times a year
daily--> 365 times a year