Question

Steven wants to start an IRA that will have $375,263 in it when he retires in 30 years. How much should he invest quarterly in his IRA to do this if the interest is 5.5% compounded semiannually? Assume an Annuity Due. Round to the nearest cent.

Answer 1

An annuity due assumes the beginning balance to be P, ordinary annuity assumes the beginning balance is 0 ... from the other one we tried :)
\[A=Pk^n+P\frac{1-k^n}{1-k}\]
\[A=P(k^n+\frac{1-k^n}{1-k})\]
\[\frac{A}{k^n+\frac{1-k^n}{1-k}}=P\]
in this case, n = 30*4, and k = 1+.055/4

Answer 2

is abt 1223 an option?

http://www.wolframalpha.com/input/?i=%5Cfrac%7B375263%7D%7Bk%5E%2830*4%29%2B%5Cfrac%7B1-k%5E%2830*4%29%7D%7B1-k%7D%7D%3B+k%3D1%2B.055%2F4