One person starts a Formal investment club by establishing a stock “mutual fund” manged by the club. and invests $1000 at the end of Year I in the fund. Each year thereafter for nine years, one new member is added to the club. Each member invests $1000 each year un the mutual fund in the name of the club, thereby creating an arithmetic gradient series of deposits. Thus. at the end of Year 10. an increment of $10 000 is added to the mutual fund compounds at a 10% annual rate. At the end of Year 11, the club stops contributing and instead withdraws an amo unt A1 I such that if withdrawals in crease at a 3% annual rate (geometric growth), the fund will be exhausted at the eud of Year 20. Note that the fund coninues In earn a return of 10% through Year 20.
(a) Draw the cash flw diagram.
(b) What is the amount. A1 , that should be withdrawn at the end of Year 11?
(c) To what percentage of the amount, AI , is the first club member entitled ?
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