4. Many retired people buy annuities. With an annuity, a saver pays an insurance company a lump- sum amount in return for the company's promise to pay a certain amount per year until the buyer dies. With an ordinary annuity, when the buyer dies, there is no final payment to his or her heirs. Suppose that at age 65, David Alexander pays $180,000 for an annuity that promises to pay him $20,000 per year for the remaining years of his life. (a) If David dies 20 years after buying the annuity, write an equation that would allow you to calculate the interest rate (yield to maturity) that David received on his annuity. (b) If David dies 17 years after buying the annuity, will the interest rate be higher or lower than if he dies after 20 years? Briefly explain.
4. Many retired people buy annuities. With an annuity, a saver pays an insurance company a lump- sum amount in return for the company's promise to pay a certain amount per year until the buyer dies. With an ordinary annuity, when the buyer dies, there is no final payment to his or her heirs. Suppose that at age 65, David Alexander pays $180,000 for an annuity that promises to pay him $20,000 per year for the remaining years of his life. (a) If David dies 20 years after buying the annuity, write an equation that would allow you to calculate the interest rate (yield to maturity) that David received on his annuity. (b) If David dies 17 years after buying the annuity, will the interest rate be higher or lower than if he dies after 20 years? Briefly explain.
Chapter5: The Time Value Of Money
Section: Chapter Questions
Problem 39P
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Transcribed Image Text:4. Many retired people buy annuities. With an annuity, a saver pays an insurance company a lump-
sum amount in return for the company's promise to pay a certain amount per year until the buyer
dies. With an ordinary annuity, when the buyer dies, there is no final payment to his or her heirs.
Suppose that at age 65, David Alexander pays $180,000 for an annuity that promises to pay him
$20,000 per year for the remaining years of his life.
(a) If David dies 20 years after buying the annuity, write an equation that would allow you to
calculate the interest rate (yield to maturity) that David received on his annuity
(b) If David dies 17 years after buying the annuity, will the interest rate be higher or lower than
if he dies after 20 years? Briefly explain.
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