You would like to establish a fund that will be used to offer a scholarship each year to a worthy student at your alma mater. You would like the total annual award to be $5,000, with the first
Award to be presented next year. Your alma mater is able to invest the funds at a constant,
Annual, tax-free rate of 8%. How much must you donate today to fund this award? Round
Your answer to the nearest dollar.

Question

Quizplus · Accepted Answer

The present value of an annuity is given by the formula:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present valuePMT is the annual paymentr is the annual interest raten is the number of yearsIn this case, we have:PMT = $5,000r = 8% = 0.08n = infinity (since the scholarship will be awarded every year forever)Plugging these values into the formula, we get:PV = $5,000 * [1 - (1 + 0.08)^-infinity] / 0.08PV = $5,000 * [1 - 0] / 0.08PV = $5,000 * 12.5PV = $62,500Therefore, you must donate $62,500 today to fund this award.

You Would Like to Establish a Fund That Will Be