Topic
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ANNUITIES |
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Team members |
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Name:
Olga Malakhouskaya
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Overview |
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A series of equal
deposits or payments made at equal intervals of
time is called an annuity. The time
between deposits is called a compounding
period. Example: If you deposit $100
into a savings account at the end of each month
at 4.5% interest, how much money are you going
to have after a year? To answer this question
you need to find the amount of the annuity.
But suppose you
want to receive payments of $1200 every month
for a year. How much money do you need to
deposit now at 5% interest? To answer this
question you need to find the present value
of an annuity. Present value is the amount
of money to be invested to obtain a specific
amount in the future.
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Study Tips,
Methods and or Advice |
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Formulas to
use:
Amount of the
annuity
A
- the amount of the annuity
R - the deposit made at the end of each period
i - interest rate
n - number of periods
Present value
of an annuity
P
- present value of an annuity
R - the deposit
made at the end of each period
i - interest rate
n - number
of periods
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Sample Questions and complete solutions
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Questions |
Complete Solutions |
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1. Calculate the
amount of the annuity, if $500 is
invested monthly for 6 years at 5.4%
interest.
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We need to adjust
the interest rate. You earn 5.4%
annually, but to use the formula the
interest should be calculated monthly.
To find the monthly interest you divide
5.4% into 12 month. You8 earn 0.45%
interest every month.
A=?
R=500
i =0.054=0.0045
12
n =6x12=72
A=42404.75
The amount of the
annuity would be $42404.75
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2. A deposit of
$5,000 is made every 6 month at 7 %
interest compounded annually. What is
the amount of the annuity after 6 years?
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In order to use the
formula we need to adjust the number of
compounding periods, because interest is
compounded annually and payments are
made semi-annually. We have to divide 7%
by 2 to find out the semi-annual
interest and multiply the number of
years by 2 to figure out the number of
compounding periods.
A=?
R=5,000
i =0.07/2=0.035
n =6x2=12
A=73009.81
The amount of the
annuity is $73009.81
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3. How much money
do you need to invest now at 4%interest
to be able to withdraw $500 every month
for five years?
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P
=? R
=500
i = 0.04= 0.0033
12
n = 5x12=60
P=27176.16 you will
need to invest $27176.16
You will need
$27176.16
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4. Marry wants to
receive $1000 monthly payments for 3
years. How much money does she need to
invest now at 5% interest?
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P=R[1-(1+i)^-n]
P =?
i R
=1000
i = 0.05=0.004166667
12
n = 3x12=36
P=1000[1-(1+0.004166667)^-36]
0.004166667
P=33365.70
Marry needs to
invest $33365.70
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Extra
Practice Questions and Answers |
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Extra Practice Questions |
Answers |
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1. Johnny decided
to start saving his money. He is going
to deposit $250 every month into his
saving account at 4.3% interest
compounded monthly. How much money is he
going to have after a year?
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3059.78 |
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2. Suppose you open
a savings account and deposit $3000
every 3 month at 6% interest compounded
annually. How much money will you have
after 3 years?
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39123.63
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3. Karl wants to
save $10,000 for his college education.
How much money does he need to invest
every month at 3% interest if he has 3
years?
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265.81 |
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4. How much money
do you need to have now to be able to
withdraw $500 every month for the next 6
years? The interest rate is 6%.
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30169.76 |
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5. Sarah has
$12,000 in her bank account right now.
Her account pays 3% interest. Suppose
she wants to withdraw money for the next
6 month until the money in the account
run out. How much can she withdraw every
month?
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2017.54 |
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Self
Reflection |
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Personal Reflection -
Olga
This was a very fun
course. I learned a lot this year. I found
financial mathematics the most interesting. It
is going to be very useful in the future. Ms.
Demakopoulos is a very good teacher and I hope
to have her next year.
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