Someone plans to deposit $3,000 per year at the end of the year for
the next 30 years into an IRA account that currently pays 7%. How much
will Daniel have on deposit at the end of 30 years?

Hi!!


Here we must calculate the future value of an annuity 

We need to use the following formula:

FV = PMT * [( 1 + i )^N - 1] / i

FV = future value (maturity value)
PMT = payment per period
i = interest rate in percent per period
N = number of periods


In this problem:

PMT = $3,000
i = 0.07
N = 30

Then:

FV = PMT * [( 1 + i )^30 - 1] / i =
   = $3,000 * [(1.07)^30 - 1] / 0.07 =
   = $3,000 * [7.612255 - 1] / 0.07 =
   = $3,000 * [6.612255] / 0.07 =
   = $283,382.36


Daniel will have on deposit $283,382.36 at the end of 30 years.


For references see:
"Anything but Ordinary: Calculating the Present and Future Value of
Annuities" by Shauna Croome:
http://www.investopedia.com/articles/03/101503.asp

I hope that this helps you. Feel free to request for a clarification
if you need it.

Regards.
livioflores-ga