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.

Question

amistre64 · Answer

you basically want to loan yourself money ... how would you calculate the monthly payments if you took out a loan with that information?

amistre64 · Answer

Bn = Bo k^n - P(1-k^n)/(1-k)

assuming we want a balance of 0 after n periods

0 = Bo k^n - P(1-k^n)/(1-k), and solving for P

Bo k^n = P(1-k^n)/(1-k)

Bo k^n(1-k)/(1-k^n) = P

amistre64 · Answer

k is the compounding interest stuff so in this case its (1+.075/12)  and n=18*12

amistre64 · Answer

so, 75000k^(18*12)(1-k)/(1-k^(18*12)), k=(1+.075/12) http://www.wolframalpha.com/input/?i=75000k%5E%2818*12%29%281-k%29%2F%281-k%5E%2818*12%29%29%2C+k%3D%281%2B.075%2F12%29 about 634 id say

amistre64 · Answer

of course your class might want you to use their formulas and tables ... but i never liked them :)

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.
a.
	
$164.98
	
c.
	
$166.21
b.
	
$165.30
	
d.
	
$167.52

anonymous · Answer

This class is confusing! None of this makes any sense!

amistre64 · Answer

hmm, let me review my thoughts and see if its still correct

amistre64 · Answer

.075 is good, 12 months a year .... for 18 years

amistre64 · Answer

1 + 2 + 3 + ... + n-1
   -2    -3  - ...  - n-1 -n
---------------------
1-k^n is fine

amistre64 · Answer

75000 = P(1-k)/(1-k^n)

thats better, 164.98

amistre64 · Answer

i was compounding a balance that did not exist instead of working up to it i spose.  we dont have the 75000 compounding since we didnt actually take a loan out.

anonymous · Answer

Thank you! (:

amistre64 · Answer

sure :)