10 Mathematics 2015 Simple Interest You need to be able to use the simple interest formula to find INTEREST PRINCIPAL INTEREST RATE per annum TIME years You also need to be able to convert time not given in years ID: 363168
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Slide1
Simple Interest
10 Mathematics 2015Slide2
Simple Interest
You need to be able to use the simple interest formula to find
INTEREST ($)
PRINCIPAL ($)
INTEREST RATE (% per annum)
TIME (years)
You also need to be able to convert time not given in years (
ie
. months, days, weeks) to a fraction of a year, and use this to find the 4 variables aboveSlide3
Simple Interest - What is it?
If you borrow money, you must pay for the use of that money. If you lend money, you will be paid for doing so. The price of borrowing or lending money is called
interest
. The simplest type of interest is called
simple interest
.
Suppose that we borrow $500 from a friend, and agree to pay him 10% interest for one year, after which time both the amount borrowed and the interest will be repaid. What does this mean? It means we will pay our friend $500, plus 10% of the amount borrowed, or
at
the end of the
year
a total of $550.
If
the money is borrowed or invested for several years, then interest may be paid or charged
more
than once. For example, if interest of 10% is charged
per annum
, then 10% of the amount borrowed is charged each year until the loan is repaid. Slide4
Simple Interest
calculating interest (I)
Simple Interest Formula
To calculate
simple interest (I)
, we need to know
the
amount
invested or borrowed (P)
, the
interest rate
% (r) and the length of time (t) for which the money is invested or borrowed.
Example:
What is the simple interest paid on $
2000 invested at 6% per annum for four
years?
P = $2000
r = 6 % per annum
(this means 6% a year is paid in interest)
t = 4 years
(this needs to be in years or a fraction of a year)
I = ?Slide5
What is the simple interest paid on $
2000 invested at 6% per annum for four
years?
P = $2000
r = 6 % per annum
t = 4 years
I = ?
Simple Interest Formula
Simple Interest paid on the investment was $480Slide6
Simple Interest
calculating the principal (P)
Simple Interest Formula used to find principal (P)
Sometimes you want to know the amount that has been borrowed or invested (P). This means we need to rearrange our formula to make P the subject. See the equation on the side.
Example:
Over a period of five years an investment earned $1070.25 at a simple interest rate of 5.45% per annum. What was the original amount deposited?
P = ?
r = 5.4% per annum
t = 5
I = $1070.25Slide7
Example:
Over a period of five years an investment earned $1070.25 at a simple interest rate of 5.45% per annum. What was the original amount deposited?
P = ?
r = 5.4% per annum
t = 5
I = $1070.25
The original amount deposited was $3 963.89
Simple Interest Formula used to find principal (P)Slide8
Simple Interest
calculating the interest rate (r)
Simple Interest Formula used to find rate (r)
Sometimes you want to know the amount that has been borrowed or invested (P). This means we need to rearrange our formula to make P the subject. See the equation on the side.
Example:
To buy his first car, Gary took out a personal loan for $3500. He paid it back over a period of
two
years and this cost him $1085 in interest. At what simple interest rate was he charged?
P = $3500
r = ?
t = 2 years
I = $1085Slide9
Example:
To buy his first car, Gary took out a personal loan for $3500. He paid it back over a period of two years and this cost him $1085 in interest. At what simple interest rate was he charged?
P = $3500
r = ?
t = 2 years
I = $
1085
The simple interest rate Gary borrowed at was 15.5%
Simple Interest Formula used to find rate (r)Slide10
Simple Interest
calculating the time invested (t)
Simple Interest Formula used to find time (t)
Sometimes you want to know the amount that has been borrowed or invested (P). This means we need to rearrange our formula to make P the subject. See the equation on the side.
Example:
If John invests $20 000 at 10% per annum until he has $32 000, for how many years will he have to invest the money?
P = $20 000
r = 10% per annum
t = ?
I = ($32 000 - $20 000) =
$12 000Slide11
Example:
If John invests $20 000 at 10% per annum until he has $32 000, for how many years will he have to invest the money?
P = $20 000
r = 10% per annum
t = ?
I = ($32 000 - $20 000) =
$12 000
John would have to invest for 6 years
Simple Interest Formula used to find time (t)Slide12
Simple Interest – more complicated
Sometimes within simple interest questions you might be
given a time period that is not a year, before finding simple interest you need to convert this time into a fraction of a year.
Example:
What is the simple interest on $
10 000 invested at 6% per annum for eight months
P =
$10 000
r = 6 % per annum
t = of a year
I = ?