Your responses must contain the following to receive full credit: 1-Cash flow di
ID: 2417972 • Letter: Y
Question
Your responses must contain the following to receive full credit:
1-Cash flow diagram of your problem
2-Specify the model/equation used [e.g. P=F(1+i)-N ]
3-Specify the values of each parameter [e.g. i=0.05 or 5% ]
Answer the question of the problem with a complete sentence that includes your numerical justification.
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1. (9 pts) A very successful alum from our department wants to establish a $10,000 scholarship to be given every year to a deserving student. If this alum wants this annual scholarship to go on forever, and the interest rate for the scholarship endowment account is 4.5%, how much money will need to be donated into this account today to accomplish this goal?
Explanation / Answer
1. Cash flow Diagram:
EOYCF $10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000
_______!___________!__________!_________!__________!__________!_________!_________!_
Year 0 1 2 3 4 4 5 6 infinity !
Initial deposit $222,222.22
NOTE: EOYCF =End of year cash flows
2. Amount to be deposited into the account today is nothing but present value of perpetuity. That can be found with the help of the following formula
Present valeu of perpetuity = C/R. where C = cashflows per period, here that is $10,000; R = Interest rate per paymetn period i.e 4.5%
Present value of Perpetuity = $10,000/4.5% = $ 222,222.22
Hence, the initial deposit to be made to give $10,000 schalorship every year is $ 222,222.22
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