Question 7 15 points Save Answer Lotteries often give you the option of taking a

Question

Question 7 15 points Save Answer Lotteries often give you the option of taking a lump-sum payment now or a fixed amount every year for, say, 10 years. For this question, assume that the yearly payments are $22,377 each year for 10 years. The first payment is made immediately, so it is not discounted, and subsequent payments are made every year thereafter. How big does the one-time lump sum payment have to be for you to take it rather than the 10-year payout? The lump sum is given immediately, so it is also not discounted. Use a discount rate of 4.3%.

Explanation / Answer

The formula for computing the present value of an annuity, when 1 installment is paid immediately, is PV = P(1+r)[1-(1+r)-n]/r where P is the periodic payment, r is the rate of interest per period and n is the number of periods. Here, P = $22,377, r = 4.3/100 = 0.0043 and n = 10. Then PV = 22377(1+0.0043)[1-(1.0043)-10]/0.0043 = 22377(1.0043)/0.0043[1-(1.0043)-10] = (22473.2211/0.0043)(1-0.9579997) = 5226330.488*0.0420003= $ 219507.45 ( on rounding off to the nearest cent). Thus, the one time lumpsum payment has to be $ 219507.45 if taken instead of a 10 year payout.

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