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(Solved): The University of Edmonton received a donation from a wealthy individual. Some of the donated money ...


The University of Edmonton received a donation from a wealthy individual. Some of the donated money will be set aside to create a scholarship fund that will pay out $10,000 at the end of every 6 months, in perpetuity. If the invested funds can earn 8% compounded semi-annually, instead of 5% compounded semi-annually, how much less money must they set aside today to pay out a $10,000 scholarship? Round your answer to 2 decimal places if needed.



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To determine how much less money the University of Edmonton must set aside today if the invested funds earn    compounded semi-annually instead of    compounded semi-annually, we can use the concept of the present value of an annuity.



Start by calculating the present value of a $10,000 scholarship payment at a 5% interest rate. The payment occurs every 6 months indefinitely.

Using the formula for the present value of an ordinary annuity:

  

where PV is the present value, PMT is the payment amount, and r is the interest rate per period, we can calculate the present value at 5%:

  

  

  



Therefore, the University of Edmonton needs to set aside    at a    interest rate to pay out a    scholarship every 6 months in perpetuity.

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