1) Suppose you just won the state lottery, and you have a choice between receivi
ID: 2757623 • Letter: 1
Question
1) Suppose you just won the state lottery, and you have a choice between receiving $2,075,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.
11.10%
10.38%
12.14%
9.44%
11.83%
2)
Sam was injured in an accident, and the insurance company has offered him the choice of $49,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity?
$437,070.42
$576,560.98
$506,815.70
$427,771.05
$464,968.53
3)
You have a chance to buy an annuity that pays $28,000 at the beginning of each year for 5 years. You could earn 4.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?
$128,450.72
$118,174.66
$120,743.68
$129,735.23
$98,907.05
11.10%
10.38%
12.14%
9.44%
11.83%
Explanation / Answer
(1) 9.44%
Present value of the two amounts are equal.
$2,075,000 = $250,000 x PVIFA(R%, 20 years)
PVIFA(R%, 20 years) = 8.3
From PVIFA table for year = 20, we find that 8.3 corresponds to an interest rate just below 10%. Among given choices, only 9.44% fits.
(2) $464,968.53
Required lump-sum = Present value of the annuity
= $49,000 x PVIFA(7.5%, 15 years) x 1.075 [Since this is annuity due]
= $49,000 x 8.8271 x 1.075
= $464,967.5
** The slight difference is due to rounding-off.
NOTE: First 2 questions are answered.
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