Question

Today is Rachel’s 30th birthday. Five years ago, Rachel opened a brokerage account when her grandmother gave her $25,000 for her 25th birthday. Rachel has added $400 to this account each month beginning the month after her 25th birthday. Rachel wants to know how much she needs to add to this account to reach her goal of $400,000 in the account by her 40th birthday. Starting one month from today, she plans to contribute a fixed amount to the account each month. The final contribution will occur on her 40th birthday. Complicating things somewhat is the fact that Rachel plans to withdraw $20,000 from the account on her 35th birthday to pay for a round the world trip. How large does each of these monthly contributions have to be for Rachel to reach her goal? Assume that the account has earned (and will continue to earn) an annual return of 12% a year, compounded monthly.

Answer 1

=(400000-25000*(1+12%/12)^(12*15)-400/(12%/12)*((1+12%/12)^(12*5)-1)*(1+12%/12)^(12*10)+20000*(1+12%/12)^(12*5))*(12%/12)/((1+12%/12)^(12*10)-1)
=776.48800