Mr. Smith sells a piece of real estate to his daughter and son-in-law in exchange for a private annuity payout. At the time of the sale, Mr. Smith has a life expectancy of 20 more years. How long will the couple be required to make payments to Mr. Smith? Question 37 options: a) 10 years. b) 5 years. c) Until Mr. Smith's death. d) 20 years (Mr. Smith's life expectancy).
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A private annuity is a financial arrangement where one party (the annuitant) receives regular payments from another party (the obligor) in exchange for an asset, typically until the annuitant's death. Show more…
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Smith is currently 45 years old and her spouse is 55 years old. As long as Smith survives, Smith will contribute $10,000 at the start of each year to a deferred life-annuity plan, starting now (at age 45) with the last scheduled contribution being when Smith is 64. The annuity will have annual payments and is scheduled to begin 20 years from now. Their joint mortality follows the LTAM Life Table with an interest rate of 5%. In each of the following cases, the life annuity value is actuarially equivalent to the value of the contributions. (a) (2 points) Suppose that the annuity will begin as scheduled if both Smith and her spouse are alive at the scheduled annuity start date. Suppose also that the annuity will pay $C per year, payable as long as both Smith and her spouse survive, and the annuity will terminate after the first death. Calculate C. (b) (2 points) Suppose that the annuity will begin as scheduled if both Smith and her spouse are alive at the scheduled annuity start date. Suppose also that the annuity will pay $D per year, payable as long as both Smith and her spouse survive, and the annuity will continue after the first death at a rate of $1 per year as long as the survivor is alive. Calculate D. (c) (2 points) Suppose that the annuity will begin as scheduled if at least one of Smith and her spouse are alive at the scheduled annuity start date. The annuity will pay $E per year as long as at least one of them survives. Calculate E.
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