Question

Today is Rachel's 30h birthday. Five years ago, Rachel opened a brokerage account when her grandmother gave her $25,000 for her 25h birthday. Rachel added $2,000 to this accou on her 26th birthday, $3,000 on her 27th birthday, $4,000 on her 28th birthday, and $5,000 on her 29th birthday. Rachel's goal is to have $400,000 in the account by her 40h birthday. tarting today, she plans to contribute a fixed amount to the account each year on her birthday. She will make 11 contributions, the first one will occur today, and the final contribution Il 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 finance the down payment on home. How large does each of these 1 1 contributions have to be for Rachel to reach her goal? Assume the account has earned (and will continue to earn) an effective return of 12% a

Answer 1

Amount already contributed to the brokerage account= $(25000+2000+3000+4000+5000) = $39000

Amount of 39000 deposited will have interest compounded annually

let the contribution per annum = x

11 x+(11 x+39000)*12%-20000-20000*12%+121128=400000

11 x+ 27.26 x + 96664-20000-3372+ 121128= 400000

38.26 x+194420=400000

38.26 x= 205580

x= 5380

therefore, amount to be invested is $5380