Bob just celebrated his 20th birthday today (1 January) and wishes to ac- cumulate $4,000,000 by the time he retires at age 65. He has two main investment streams to accomplish this goal:
ˆSave 10% of his after-tax salary every month. As of this today, he is earning $3,000 after-tax at the end of each month and estimates his after-tax salary will increase by about 5% annually for the first ten years (i.e., years = 0,1,...,10; note that in Year 0, he is earning
$3,000), and then by about 3% annually for the rest of his career (i.e., years = 11,12,...,64; he retires in Year 65). He will set this money aside in an interest-free cheque account.
ˆInvest $P monthly at the beginning of each month in a high interest hedge fund for the next 45 years that has i(12) = 6%. Note that the month he turns 65 is excluded.
What value should P, rounded to the nearest dollar, be so that he meets his $4,000,000 investment target by age 65?