Question to be solved from CFA Level 1 mock – Perpetuity

Question

Kindly help me in answering the following question:Reena, a
successful inventor has decided to set up a scholarship fund for deserving at
her Alma matter. Her plan is for fund to the capable of awarding $25000
annually in perpetuity the first scholarship is to be awarded and paid out
exactly four years from today. The fund will be deposited into an account
immediately and will grow at a rate of 4%, compounded semiannually for the
foreseeable future. How much money must the inventor donate today to fund the scholarship?

a.      
$545,789

b.     
$549,487.

c.      
$543,254

krishTa · Answer

This can be solved in 2 steps.Time line 1 -> What is the amount that Reena need to deposit to award $25,000 annually @ 4% semi annually, starting from next yearStep 1 -> calculate Effective Annual rate which is ((1 + r/m)^m) -1. Hence EAR = ((1+0.04/2)^2) -1 = 4.04%Step 2 -> PV of a perpetuity where annual return is $25,000 and rate of return is 4.04% is A/r = 25,000/0.0404 = 618,811.88Time line 2 -> What is the amount that Reena needs to deposit now so that the deposit is 618,811.88 by the end of 3 years @4% semi annuallyThis is simple TVM problem where FV = 61,8811.88, r = 4.04, N = 3. I got the answer $549,487.24Option b.Hope I am correct