You are the recipient of a gift that will pay you $25,000 one year from now and every year thereafter for the following 24 years. The payments will increase in value by 2.5 percent each year. If the appropriate discount rate is 8.5 percent, what is the present value of this gift?

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Quizplus · Accepted Answer

This is a growing annuity problem where the first payment is $25,000, the growth rate of the payments is 2.5%, and the discount rate is 8.5%. The formula for the present value of a growing annuity is PV = P * [(1 - (1 + g)^n / (1 + r)^n) / (r - g)], where P is the first payment, g is the growth rate, r is the discount rate, and n is the number of periods. Plugging in the values: P = $25,000, g = 2.5% or 0.025, r = 8.5% or 0.085, and n = 25, we find the present value. The correct calculation aligns with option B, $316,172, after applying the formula correctly.

You Are the Recipient of a Gift That Will Pay