How much will it cost to purchase a 20-year indexed annuity in which the end of quarter payments start at $6,000 and grow by 0.5% every quarter? Assume that the money used to purchase the annuity earns 8% compounded quarterly.

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Quizplus · Accepted Answer

The correct answer is A because the present value of the annuity is $277,727. The present value of an indexed annuity can be calculated using the following formula:PV = PMT * (1 - (1 + g)^-n) / (r - g)where:PMT = the starting paymentg = the growth raten = the number of paymentsr = the discount rateIn this case, the starting payment is $6,000, the growth rate is 0.5%, the number of payments is 80 (20 years * 4 quarters per year), and the discount rate is 8%. Plugging these values into the formula, we get:PV = $6,000 * (1 - (1 + 0.005)^-80) / (0.08 - 0.005)= $277,727

How Much Will It Cost to Purchase a 20-Year Indexed