chrissytt17
a person wishes to invest M dollars at t eh end of each month from January 2000 until the end of December 2003. If the account gives interest at the annual rate of 18% compounded monthly and the individual wishes to have $100,000 by the end of 2003, how much should be invested each month?
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chrissytt17
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No i don't
sheg
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it is
\[A=P\times{(1+r)^{n}}\]
where A = Amount
P = Principal
r = Rate of interest
n = number of time period
sheg
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ok now tell me for how many moths you will be investing??
chrissytt17
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so for 3 years that's 36 months
sheg
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you started investing from Jan 200 - Dec 2003
right it is 36 months
chrissytt17
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A=100,000x(1+18%)^36
chrissytt17
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a=100,000 (19)^36
sheg
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so here n = 3yrs = 36 months
r = 18% per annum
but this will get compounded monthly so
it cannot be 18%
chrissytt17
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can i leave it in the annual form and just do
A=100,000x(19)^3
?
sheg
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so your formula will change right the formula that i had given u is the general formula
now when it is compounded monthly in that case the formula would be
\[A = P\times{(1+{{r}\over{12}})^{12n}}\]
sheg
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@chrissytt17 here principal is unknown
sheg
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are you getting my point?
chrissytt17
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i thought the principal is the amount that the individual wants
sheg
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no what you want that you will get at what time????
sheg
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the individual wishes to have $100,000 by the end of 2003, how much should be invested each month?
chrissytt17
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100,000=Px(1+r/12)^12n
sheg
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where r = 18%
but when you are plugging in the value of r that time convert it into decimal
so r = 0.18
chrissytt17
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100,000= P x (1+.18/12)^12*3
?
chrissytt17
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100,000= P x (1.015)^36
chrissytt17
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am i on the right track?
sheg
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wait let me cross check it
chrissytt17
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i came up with about 58,513.75
sheg
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no it is not correct
chrissytt17
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I followed the formula
chrissytt17
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I think I am lost
sheg
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hey i was not telling you about the Annuity do you know about it?
chrissytt17
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no
sheg
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you are in which class
chrissytt17
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math 118
sheg
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ok do you know about time value of money
chrissytt17
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I'm not sure
sheg
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\[100000 = P \times \sum_{n=1}^{36}(1.015)^n\]\]
sheg
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ok solve this one you will get the exact value
sheg
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the second factor on RHS is called as Present Value Interest Factor of Annuity
chrissytt17
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I don't know what that symbol is
sheg
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it is summation