Question 1200182
<pre>
Francine currently has $45,000 in her 401k account at work, and plans to contribute $800 at the end of each month for the next 15 years. How much will she have in the account in 15 years, if the account averages a 6% annual return? Assume monthly compounding. 

For the $45,000 BEGINNING amount, use the FUTURE VALUE formula of $1: 
   {{{matrix(1,3, A, "=", P(1 + i/m)^(mt))}}}, where: {{{A}}} = Accumulated amount, or future value (Unknown, in this case)
                            {{{P}}} = Present Value||Principal invested||INITIAL amount deposited ($45,000, in this case)
                            {{{i}}} = Annual Interest rate (6%, or .06, in this case)
                            {{{m}}} = Number of ANNUAL compounding periods (Monthly, or 12, in this case)
                            {{{t}}} = Time, in years (15, in this case)


For the monthly $800 contribution, use the formula for the FUTURE VALUE of an ORDINARY ANNUITY:
   {{{FV[oa] = PMT * ((1 + i/m)^(mt) -1) * (m/i)))}}}, where:  {{{FV[oa]}}} is the future value in the amount of time (years), or the amount that will
                                                   be available then <font color="red"><b>(UNKNOWN, in this case)</font></b>
                                             {{{PMT}}} is the payment amount <font color="red"><b>($800, in this case)</font></b>
                                               {{{i}}} is the interest rate, per year <font color="red"><b>(6%, or .06, in this case)</font></b>
                                               {{{m}}} is the number of compounding periods per year <font color="red"><b>(12, in this case)</font></b>
                                               {{{t}}} is the amount of time the money is invested <font color="red"><b>(15, in this case)</font></b>

<font color="blue"><font size = 4><b>You then ADD "A" to FV<sub>oa</sub> to get the amount in the account after 15 years</font></font></b>.</pre>