# SOLUTION: 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

Algebra ->  Algebra  -> Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: 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       Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Percentage and Pie Charts Solvers Lessons Answers archive Quiz In Depth

 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?Found 2 solutions by stanbon, gromo:Answer by stanbon(57328)   (Show Source): You can put this solution on YOUR website!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? ---------------- EQUATION: Let "x" be the number of years. (42180.53+5000x)(1.12x)=250000 5600x^2+47242.1936x-250,000=0 I graphed this and found x=3.68 years You might want to round that out to 4 yrs. Cheers, Stan H. Answer by gromo(1)   (Show Source): You can put this solution on YOUR website!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. 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. To find the FV of an annuity: FV= c*((1+r)^n-1)/r = 5000*(1.12^n-1)/0.12 To find the FV of a lump sum: FV= c*(1+r)^n = 42180.53*(1.12)^n Now: \$250,000 = 5000*(1.12^n-1)/0.12 + 42180.53*(1.12)^n Since calculations are complicated, I have used excel to answer the problem, but you can use a financial calculator as follows: Using your financial calculator, enter the following data: I = 12; PV = -42180.53; PMT = -5000; FV = 250000; N = ? Solve for N = 11. It will take 11 years for John to accumulate \$250,000.