Many retired people buy annuities. With an annuity, a saver pays an insurance company, such as Berkshire Hathaway Insurance Company or Northwestern Mutual 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 $100,000 for an annuity that promises to pay him $10,000 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 that David received on his annuity.
b. If David dies 40 years after buying the annuity, will the interest rate be higher or lower than if he dies after 20 years? Briefly explain.