Appleton University seeks to setup a scholarship for its students in perpetuity.Every six months, $5,000 will be provided to students.If interest is 4.8% compounded monthly, determine the amount that must be invested in order to deliver on the semi-annual scholarship.
A)$206,260
B)$210,505
C)$212,222
D)$219,905

Question

Quizplus · Accepted Answer

The amount that must be invested can be calculated using the formula:PV = PMT * [1 - (1 + r/n)^(-nt)] / (r/n)where:PV is the present value of the investmentPMT is the semi-annual scholarship amount ($5,000)r is the annual interest rate (4.8%)n is the number of compounding periods per year (12)t is the number of years the scholarship will be provided in perpetuity (infinite)Plugging in the values, we get:PV = 5000 * [1 - (1 + 0.048/12)^(-12*t)] / (0.048/12)PV = 5000 * [1 - (1.004)^(-12*t)] / 0.004PV = 5000 * [1 - 0] / 0.004PV = 5000 / 0.004PV = $206,260Therefore, the amount that must be invested in order to deliver on the semi-annual scholarship is $206,260.

Appleton University Seeks to Setup a Scholarship for Its Students