Andrew Bogut just received a signing bonus of $1,000,000. His plan is

QUESTION

Andrew Bogut just received a signing bonus of $1,000,000. His plan is to invest this payment in a fund that will earn 8%, compounded annually.Instructions(a) If Bogut plans to establish the AB Foundation once the fund grows to $1,999,000, how many years until he can establish the foundation?(b) Instead of investing the entire $1,000,000, Bogut invests $300,000 today and plans to make 9 equal annual investments into the fund beginning one year from today. What amount should the payments be if Bogut plans to establish the $1,999,000 foundation at the end of 9 years?
a) Using equation of future value of single amount: FV = Amount*(1+i)^n 1999000 = 1000000*(1+.08)^n n = 9 Accordingly it will take 9 year to accumulate the target fund and establish the ABfoundation. b) Accumulated value of todays investment after 9 years: FV = 300000*(1+.08)^9 FV= 599701 Remaining money to be accumulated from annual contributions = 1999000 -¦

701 = 1399299 Now we will apply the equation of future value of annuity to find out amount of annual investment amount, accordingly: FV = A*[(1+r)^n-1]/r 1399299 = A*[(1+.08)^9-1]/.08 A = 112055 Accordingly annual amount to be invested is 112055.

ANSWER:

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