an annuity versus a single amount Personal Finance Problem Assume that you just
ID: 1172441 • Letter: A
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an annuity versus a single amount Personal Finance Problem Assume that you just won the state lottery. Your prize can be taken ether in the form of $34,000 at the end of each of the next 25 years ?at is, s850,000over 25 years) or as a sngle amount of S545 000 paid immediately aif you exped to be able to eam 7% annualy on your investments over the next 25 years, innng taxes and other considerations, which atemat eshold you ale? why? t. Would your deasion in part a dange if you could earn 9% rather than 7% on your mestments over the next 25 years? Why? c. On a strictly economic basis, at approximately what earnings rate would you be indifierent between the two plans? If you take the prize as an annuity, the present value of the 25-year ordinary annuity is sRound to the nearest cent) It you take the prize as a single amount, the present value of the lumo sum is s(Round to the nearest dolar) Which alternative should be chosen? (Select the best answer below) O Lump sum, because the present value is greater O Annual payments, because the present value is greater (Round to the nearest cent) b. " you earned 9% rather than 7% on your investments re present value ofthe 25-year ordnary annuity is Which aternative ehould be chosen? (Select the best anower below) Annual payments, because the present value is greater Lump sum becaute the present value is greater O c. on a strictly economic basis, the rate at which you would be indiferent between the two plans isExplanation / Answer
a)
Present vallue of annuity = 34,000 * [ 1 - 1 / ( 1 + 0.07)25]] / 0.07
Present vallue of annuity = $396,221.83
b)
If the interest was 9%, the present value would be even more lower. Therfore, Lump sum becaus ethe present value os greater
c)
Indifferent rate = 3.76%
Keys to use in financial calculator: PV = 545000, PMT = -34,000 , N = 25, CPT I/Y
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