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Topic
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Compound
Interest and Present Value |
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Team members |
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Name:
Sharmila Srinithiananthasing
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Overview |
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In simple
interest, interest is calculated on the
principal and it is not added to it. Even if the
amount is left for a long time. The principal
won’t get changed so the interest earned will be
the same. But in the case of compounding
interest the interest will be added to the
principal, so that in the next compounding
period the principal has been increased by the
interest earned already. So as time progresses
the principal is increasing. Therefore the
interest earned will increase as well. Suppose
that you are going to receive a lump some amount
of money in a certain period of time. How much
that money is worth today is the present value.
In other words if you put a lower amount of
money in an investment that will grow to receive
the lump some of money. Then the money that you
are investing now is your present value.
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Study Tips, Methods and or Advice |
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How to
calculate interest rate (i):
Generally the interest rates are given as per
year r%/a
Annually = 1
Semi-annually: m =2
Quarterly: m =4
Monthly: m = 12
Weekly: m= 52
Biweekly: m =26
Daily: m =365
Example:
If the interest rate is 12.25% and is calculated
weekly what is the compounding interest?
i =
How to
calculate conversion periods ( ):
Generally if the total investment period (T
years) the number of conversions is going to be
multiplied by
m
(=
T
Example:
One investment is for 5 years, and the interest
is compounded monthly. What is the conversion
some period?
m = 12
=
T
T = 5
=
  =
60
General
Equations:
Compound Interest Formula:
Where P is the present amount
or principal;
i
is the interest rate per compounding period
expressed as a decimal; it is
found by dividing the
annual interest rate by
the number of compounding periods per year; and
 is
the total number of compounding periods; it is
found by multiplying
the number of years by
the number of compounding periods per year.
Present Value Formula:
Where P = present value
i
= interest value
=
number of conversions
A = amount that
investment will grow to in the future
To find the
present value formula, we can derive it from the
compounding interest formula like so:
OR
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Sample Questions and Complete solutions |
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Questions |
Complete Solutions |
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Suppose $1000 is invested for 10
years. Calculate the compound
amount, A, under the following
circumstances.
a)
The annual interest rate is 6%,
compounded annually.
b)
The annual interest rate is 8.5%,
compounded semi-annually.
c)
The annual interest rate is 7.75%,
compounded monthly.
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a)
A = ?
P = 1000
i =
6%
à
0.06
= 10
The
compound amount (A), compounded annually
is $1790.85. |
b)
A = ?
P
= 1000
i
=8.5%à
à
0.0425
=
=
20
=
$2298.91
The
compound amount (A), compounded
semi-annually is $2298.91.
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c)
A = ?
P
= 1000
i
=7.75%à
à
0.006458333
=
=
120
=
$2165.19
The
compounding amount (A), compounded
monthly is $2165.19. |
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$100 is invested. Determine the
values of P, A, i and,
for each situation.
a)
An annual interest rate of 4%,
compounded semiannually, for 3 years.
b)
An annual interest rate of 6%,
compounded monthly, for 2 years.
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a)
A = ?
P = 100
i = 4%
à
 à
0.02
=
= 6
=
=
$112.62
The
values of P = $100
i = 0.02
=
6
A = $112.62
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b)
A = ?
P = 100
i
= 6%
à
à
0.005
=
= 24
=
=
$112.72
The
values of P = $100
i = 0.005
=
24
A = $112.72 |
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3.
Calculate the present value of $9000 in
four years at 6% per annum compounded
monthly.
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P = ?
A =
9000
i
= 6%
à
à
0.005
=
=
48
=
=
$7083.8p
The
present value is $7073.89
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P = ?
A =
9000
i
= 6%
à
à
0.005
=
=
48
=
= $7083.89
The
present value is $7083.89. |
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4.
Stephen borrows $1000 from his uncle. He
agrees to repay the loan in five years.
Stephen’s uncle tells him that he wants
the interest compounded quarterly. When
Stephen repays the loan in five years,
he owes his uncle $1485.95. What annual
interest rate did Stephen’s uncle
charge?
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A =
1485.95 Stephen’s
uncle charged him 2%
P =
1000 interest rate.
=
=
20
i
= ?
=
1.48595 =
=
(1+i)
1.020000089 = 1+ i
1.020000089-1 = i
0.020000089 = i
i =
=
2%
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Extra Practice Questions and Answers |
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Extra Practice Questions |
Answers |
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1. On
the day his son is born, Mike wishes to
invest a single sum of money that will
grow to $10,000 when his son turns 21.
If Mike invests the money at 4%/a
compounded semi-annually, how much must
he invest today?
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$4353.04 |
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2.
Tiffany deposits $9000 in an account
that pays 10%/a, compounded
quarterly. After three years the
interest rate changes to 9%/a,
compounded semi-annually. Calculate the
value of her investment two years after
this change.
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$14344.24
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Margaret can finance the purchase of
a new $949.99 refrigerator in two
ways:
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Plan A:
No money down, finance at 5%/a,
for 2 years
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Plan B:
No money down, finance at 5%/a,
compounded quarterly, for 2 years
Which
plan is better?
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Plan
A |
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4.
Noah is investing $2517 in an account
compounded monthly. He wants to have
$3000 in 3 years for a trip to Europe.
What interest rate to the nearest
hundredth of a percent compounded
monthly, does he need?
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5.87% |
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5.
Anita saved $8000 from her first job to
buy a Guaranteed Investment Certificate,
or GIC, at 5.75%, compounded annually.
How much will the GIC be worth after 2
years?
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$8946.45 |
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Self Reflection |
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Personal
Reflection - Sharmila
I thought
that designing the webpage was a really neat
idea. I thought that this assignment was really
different from all the other summative
assignments that I’ve done in any of my other
classes. This assignment allowed us to use our
creative side to explain and teach a lesson. By
doing this assignment I was able to have a much
better understanding. I also think that when we
put all the final pages together it would make
an excellent study guide for the exams.
When we first
started this topic in class I wasn’t very
interested and I thought that I was never going
to understand it. However as we went through the
chapter I began to like the chapter because it
was more interesting then I thought it would be,
thus the reason for choosing this topic. This
topic is very helpful when dealing with money
and in figuring out how much money is needed in
order to reach a certain amount or what the
total amount of money one will receive. This
topic relates to real life situations where
these formulas’s actually come in handy unlike
the other ones such as trig equations and
identities.
Overall I’d
say that having the opportunity to be able to
teach a topic in a fun and creative way makes me
want other assignments to be as fun and
interesting as this. This assignment didn’t
really restrict us to doing something one
certain way. Even though we had guidelines and
expectations as to what we should have, we were
still given the opportunity to present things
and create it in out own way.
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