Question

Each year, scholarships worth $25,000 are to be made available to the children of the company's employees. If the first

scholarships are to be offered annually starting one year from now, what amount must be invested today at 6%

compounded semi-annually to fund the scholarship program indefinitely?

Answer 1

Since the scholarship offered is indefinite therefore, it is a perpetuity. The amount that must be investeed today to fund the scholarship program indefinitely will be the present value of the perpetutiy.

Calculation of amount at which student will be indifferent if he gets semi-annual payment

Lets the amount paid semi-annually be X

Therefore X*1.03 + X = 25,000 (because X is a amount that if paid semi-annually, student should get benefit equal to 25,000. Also X is earning 1.03 after first payment at 6 month and at 12 month we will again pay X and this amount that is value of 1 year should be equal to 25,000)

Calculating for X :

X = 25000/2.03

X = 12,315.27

Semi-Annual rate = 6%/2 = 3%

Present Value of perpetuity = Amount Payable/Rate

= 12,315.27/.03 = $410,509.0312

Therefore, $410,509.0312 should be invested

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