Question

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?

Answer 1

No i don't

Answer 2

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

Answer 3

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

Answer 4

so for 3 years that's 36 months

Answer 5

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

Answer 6

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

Answer 7

a=100,000 (19)^36

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

@chrissytt17 here principal is unknown

Answer 12

are you getting my point?

Answer 13

i thought the principal is the amount that the individual wants

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

100,000= P x (1.015)^36

Answer 20

am i on the right track?

Answer 21

wait let me cross check it

Answer 22

i came up with about 58,513.75

Answer 23

no it is not correct

Answer 24

I followed the formula

Answer 25

I think I am lost

Answer 26

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

Answer 27

no

Answer 28

you are in which class

Answer 29

math 118

Answer 30

ok do you know about time value of money

Answer 31

I'm not sure

Answer 32

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

Answer 33

ok solve this one you will get the exact value

Answer 34

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

Answer 35

I don't know what that symbol is

Answer 36

it is summation