Math help, finance and interest?

Mathloser67:1 day agovia iPhone|Last edited at 9:31AM on 4/30/2013
College fund. They deposit 7500$ into an account. 6 and 3/8% for 18 years. Find future value of the account if the interest is compounded:

1.annually, quarterly, weekly, continuously #automatic A

An interesting chapter in the book e: The Story of a Number by Eli Maor.

For annually the answer is a * (1+i)^18 where a is equal to 7500 (i'll drop the $ sign for convience) and i is equal to.06375 or about 22812. For the other values you multiply the 18 by the appropriate factor and divide the i by the same factor, i.e (1+i)^18 becomes
(1 + i/n)^(18*n)
where for annually n=1, quarterly n=4, weekly n=52, and continuously n = infinity. To figure out that n equal infinity part, we note that the equation can be written as
(1 + 1 / (n/i. ^. N/i) * ( 18 * i )
or, letting n go to infinity and using a well know formula for e
e^(18 i)
or about 23627.

The book has many other interesting facts about the number e and I've found it a great read.