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?

- anonymous

- jamiebookeater

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- anonymous

No i don't

- anonymous

it is
\[A=P\times{(1+r)^{n}}\]
where A = Amount
P = Principal
r = Rate of interest
n = number of time period

- anonymous

ok now tell me for how many moths you will be investing??

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- anonymous

so for 3 years that's 36 months

- anonymous

you started investing from Jan 200 - Dec 2003
right it is 36 months

- anonymous

A=100,000x(1+18%)^36

- anonymous

a=100,000 (19)^36

- anonymous

so here n = 3yrs = 36 months
r = 18% per annum
but this will get compounded monthly so
it cannot be 18%

- anonymous

can i leave it in the annual form and just do
A=100,000x(19)^3
?

- anonymous

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
\[A = P\times{(1+{{r}\over{12}})^{12n}}\]

- anonymous

@chrissytt17 here principal is unknown

- anonymous

are you getting my point?

- anonymous

i thought the principal is the amount that the individual wants

- anonymous

no what you want that you will get at what time????

- anonymous

the individual wishes to have $100,000 by the end of 2003, how much should be invested each month?

- anonymous

100,000=Px(1+r/12)^12n

- anonymous

where r = 18%
but when you are plugging in the value of r that time convert it into decimal
so r = 0.18

- anonymous

100,000= P x (1+.18/12)^12*3
?

- anonymous

100,000= P x (1.015)^36

- anonymous

am i on the right track?

- anonymous

wait let me cross check it

- anonymous

i came up with about 58,513.75

- anonymous

no it is not correct

- anonymous

I followed the formula

- anonymous

I think I am lost

- anonymous

hey i was not telling you about the Annuity do you know about it?

- anonymous

no

- anonymous

you are in which class

- anonymous

math 118

- anonymous

ok do you know about time value of money

- anonymous

I'm not sure

- anonymous

\[100000 = P \times \sum_{n=1}^{36}(1.015)^n\]\]

- anonymous

ok solve this one you will get the exact value

- anonymous

the second factor on RHS is called as Present Value Interest Factor of Annuity

- anonymous

I don't know what that symbol is

- anonymous

it is summation

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