document.write( "Question 54687: John Roberts has $42,180.53 in a brokerage account, and he plans to contribute an additional $5,000 to the account at the end of every year. The brokerage account has an expected annual return of 12 percent. If John's goal is to accumulate $250,000 in teh account, how many years will it take for John to reach his goal? \n" ); document.write( "
Algebra.Com's Answer #384990 by gromo(1)\"\" \"About 
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The $5,000 is considered an annuity for which we want to find the FV; while the $42,180.53 is a lump sum for which we also want to find the future value after n number of years.\r
\n" ); document.write( "\n" ); document.write( "Therefore, the sum of the FV of the annuity & the future value of the lump sum should be $250,000 after n number of years.\r
\n" ); document.write( "\n" ); document.write( "To find the FV of an annuity:
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "FV= c*((1+r)^n-1)/r\r
\n" ); document.write( "\n" ); document.write( "= 5000*(1.12^n-1)/0.12\r
\n" ); document.write( "\n" ); document.write( "To find the FV of a lump sum:\r
\n" ); document.write( "\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "FV= c*(1+r)^n
\n" ); document.write( "= 42180.53*(1.12)^n\r
\n" ); document.write( "\n" ); document.write( "Now:\r
\n" ); document.write( "\n" ); document.write( "$250,000 = 5000*(1.12^n-1)/0.12 + 42180.53*(1.12)^n\r
\n" ); document.write( "\n" ); document.write( "Since calculations are complicated, I have used excel to answer the problem, but you can use a financial calculator as follows:\r
\n" ); document.write( "\n" ); document.write( "Using your financial calculator, enter the following data: I = 12;
\n" ); document.write( "PV = -42180.53; PMT = -5000; FV = 250000; N = ? Solve for N = 11. It will take
\n" ); document.write( "11 years for John to accumulate $250,000.
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