You have just won a lottery entitling you to receive, starting today, a series of 21 quarterly payments of $25,000 each

You have just won a lottery entitling you to receive, starting today, a series of 21 quarterly payments of $25,000 each, followed, one year after this series of payments ends, by a second series of annual payments of $30,000 each forever! (The first $30,000 payment is to be received exactly one year after the last $25,000 payment is received.) If the appropriate discount rate is r = 10 percent compounded continuously, what is the present value of all these future lottery payments?

Expert Solution

EAR = e^0.10 - 1 = 10.52%

APR(quarterly) = 4[(1.1052)^1/4 - 1] = 10.13%

Value of $30,000 perptuity at the end of 21 quarters = 30,000/0.1052 = $285,171.10

Calculating Value of winning today,

Using TVM Calculation,

PV = BEG[PMT = 25,000, FV = 285,171.10, N = 21, I = 0.1013/4]

PV = $571,981.51

Value today = $571,981.51

jeff jeffy answered 2 years ago

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