i need some help in annuities? any help?

Question

anonymous · Answer

annuities are based on some repetitive payment

P

P + P(k)

P + P(k) + P(k)^2

P + P(k) + P(k)^2 + P(k)^3

etc ... such that k is a calculation of interest

anonymous · Answer

do you have anything more specific?

anonymous · Answer

i really dont how to solve them thatsmy main part

anonymous · Answer

well, is there any specific problem we could work with?  the stuff i originally posted is the basics of how to approach a solution.

anonymous · Answer

Suppose that a family wants to start a college fund for their child. If you can get an APR of 7.5% and want the fund to have a value of $75,000 after 18 years, how much should you deposit monthly? Assume an ordinary annuity.

anonymous · Answer

We have a balance that we want to obtain, -75k

we have a given time period of 18 years, 12 times a year:  (18*12) payments

each payment accumulates a compound interest of (1+.075/12)

do we agree?

anonymous · Answer

there is a table method, but i dont have the tables handy so I generate a formula instead

anonymous · Answer

i agree i see where yu are coming from when yu break it down

anonymous · Answer

the stuff I posted at the start is called a geometric series:  that formualtes into:

$$0 = Bk^n + P\frac{1-k^n}{1-k}$$
B = -75000
n = 18*12
and k is that  1+.075/12, solving for P is what we want

$$0 = -75000 k^n + P\frac{1-k^n}{1-k}$$
$$75000 k^n = P\frac{1-k^n}{1-k}$$
$$75000 k^n \frac{1-k}{1-k^n}= P$$
with a little more algebra that turns into the standard textbook formula, but i jsut find this form easier to play with

anonymous · Answer

when we fill in that parts we get: http://www.wolframalpha.com/input/?i=75000+k%5E%2818*12%29++%5Cfrac%7B1-k%7D%7B1-k%5E%2818*12%29%7D%2C+k%3D%281%2B.075%2F12%29

anonymous · Answer

or its been awhile,  we want to start with a balance of 0, add to it to get up to 75000, so B=0 might be better

anonymous · Answer

my answer choices are 
a.
$164.98
c.
$166.21
b.
$165.30
d.
$167.52

anonymous · Answer

$$75000 = 0k^n + P\frac{1-k^n}{1-k}$$
yeah, that was my error i beleive

anonymous · Answer

http://www.wolframalpha.com/input/?i=75000+%5Cfrac%7B1-k%7D%7B1-k%5E%2818*12%29%7D%2C+k%3D%281%2B.075%2F12%29 thats better :)

anonymous · Answer

would that website b a good one to solve my probelms on?

anonymous · Answer

yes, if you know a good formula it will work out the maths

anonymous · Answer

i got a whole work sheet of this

anonymous · Answer

lots of practice then :)