NF Simple Interest and Compound Interest (pdf)

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Something to get you started...
Learning Intention:
Evaluate the concept of compound interest and how it impacts
the world around us.
Take out your books and open them on your
homework page. We are going to go through the
answers together
RED:
A bank is offering 2.5% simple interest on a savings account. If you deposit
$5000, how much interest will you earn in one year?
AMBER:
Bertha deposited $1000 into a retirement account when she was 18. How
much will Bertha have in this account after 50 years at a yearly simple
interest rate of 7.5%?
GREEN:
Robert deposits $ 3000 in State Bank of India for 3 years which earn him
an interest of 8%. What is the amount he gets after...
a) 1 year
b) 2 years
c) 3 years?
EXTENSION:
Nancy invested $6000 in a bond at a yearly rate of 3%. She earned $450 in
interest. How long was the money invested?
CHALLENGE:
Mr. Mogi borrowed $9000 for 10 years to make home improvements. If he
repaid a total of $20,000 at what interest rate did he borrow the money?
Sep 12­07:03
Something to get you started...
Answers:
Learning Intention:
Evaluate the concept of compound interest and how it impacts
the world around us.
Visualiser:
Comparing different ways of setting
out our calculations.
Sep 12­07:03
Number:
Percentage application
Evaluate the concept of
compound interest and how it
impacts the world around us.
Now that I can find my
multiplier....
...how can I use it?
Develop an
Illustrate
Compare the
the process
difference
of calculating
between simple
simple
and compound
around the
interest.
interest.
world.
Jun 30­15:41
understanding of
how compound
interest is used
Learning Intention:
Evaluate the concept of compound interest and how it impacts
the world around us.
Based on the discussion so far today, write down
something new that you have learnt about
dealing with percentages.
Oct 24­20:46
Learning Intention:
Evaluate the concept of compound interest and how it impacts
the world around us.
Simple Interest is mostly used as a simplified model to
help students and adults understand the principle of
calculating interest.
The standard formula(e) for calculating the interest is/are
A = P(1 + rt)
or
A = P(1 + Rt)
100
A = Total Accrued amount (principal + interest)
P = Principal amount
r = Rate of interest as a decimal
R = Rate of interest as a percentage (which we
then divide by 100 to turn it into a decimal)
t = Time period involved in months or years.
Imagine you wanted to borrow $20,000 to buy a new kitchen.
The $20,000 is the amount you will be borrowing, the principal.
The bank offers you a rate of 6% interest on the loan, this is
our rate of interest, R.
We can turn it into a decimal by dividing by 100.
r= 6
= 0.06
100
You agree to pay the bank back the $20,000 plus the interest
over 5 years or 60 months. This is the time period, t.
So, the total amount you would expect to pay the bank back is
called the Total Accrued amount, A.
Using our formula.
A = P (1 + rt)
Substituting in our numbers.
A = 20000(1 + 0.06 x 5)
= 20000 x 1.3
= $26000
Once we have paid the bank back, they will be $6000 dollars
better off
Jun 30­15:41
Learning Intention:
Evaluate the concept of compound interest and how it impacts
the world around us.
Compound Interest is a more realistic model, and takes into
account the fact that the amount you are paying off, or the
amount that you are being paid interest on, changes over time.
The standard formula for calculating the compound interest
is:
A = P(1 +
r nt
)
n
A = Future value of the investment/loan (principal + interest)
P = Principal amount (the initial deposit or loan amount)
r = Rate of interest as a decimal
t = Time period involved in months or years.
n
= the number of times that interest is compounded per year.
Let us look to borrowing the same $20,000 to buy a new kitchen.
The $20,000 is the amount you will be borrowing, the principal.
The bank offers you a rate of 6% interest on the loan, this is
our rate of interest as a percentage. As a decimal we would have
0.05.
We agree to pay back the loan over a period of 5 years, or 60
months, this is our time period. Our loan, however, is
compounded monthly.
So, the total amount you would expect to pay the bank back is
called the Total Accrued amount, A.
Using our formula.
A = P(1 +
r nt
)
n
Substituting in our numbers.
A = 20000(1 + 0.06)
12x5
12
= 20000 x (1.005)
(total number of months in 5 years)
(12 months in a year)
60
= 26,977.003050986321....
= $26,977.00 (The Dollar has 2 decimal places)
Once we have paid the bank back, they will be $6977 dollars
better off.
Jun 30­15:41
Learning Intention:
Evaluate the concept of compound interest and how it impacts
the world around us.
Simple Interest:
Imagine that you are calculating a simple interest of
5% on savings of $1000 over a period of 5 years.
At the end of the first year:
Savings = 1000(1 + 0.05) = 1050
At the end of the second year :
Savings = 1000(1 + 0.05x2) = 1100
At the end of the third year:
Savings = 1000(1 + 0.05x3) = 1150
At the end of the fourth year :
Savings = 1000(1 + 0.05x4) = 1200
At the end of the fifth year:
Savings = 1000(1 + 0.05x5) = 1250
So, for Simple interest, we are adding 5% of the
original amount each time.
ie
1000 ( 1 + 0.05 + 0.05 + 0.05 + 0.05 + ....)
A = P(1 + r x t)
A = P(1 + rt)
Jun 30­15:41
Learning Intention:
Evaluate the concept of compound interest and how it impacts
the world around us.
Compound Interest:
Imagine that you are calculating compound interest
of 5% per year on savings of $1000 over a period of
5 years.
At the end of the first year:
Savings = 1000(1 + 0.05) = 1050
At the end of the second year :
2
Savings = 1000(1 + 0.05) = 1102.50
At the end of the third year:
3
Savings = 1000(1 + 0.05) = 1157.625
= 1157.63
At the end of the fourth year :
4
Savings = 1000(1 + 0.05) = 1215.50625
= 1215.51
At the end of the fifth year:
5
Savings = 1000(1 + 0.05) = 1276.2815625
= 1276.28
So, for Compound Interest with a yearly rate, we are
adding 5% of the previous value each time.
ie
1000( 1 + 0.05) x ( 1 + 0.05) x ( 1 + 0.05) x .....
A = P x (1 + r)
A = P(1 + r)
t
t
In the real world, compound interest is calculated
multiple times during year. Sometimes 4 times a year,
but mostly 12 (ie every month).
So, we modify the formula. We split the yearly rate of
compound interest equally between the number of
installments that will be paid.
This means that over the course of the repayment,
interest will be added 5 x number of installments.
Hence, the formula:
A = P(1 +
r
n
nt
)
Jun 30­15:41
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