Q9) All of the following statements describe the operation of a life annuity EXCEPT: A. The annuitant is assured that he or she cannot outlive the length of time of the annuity payments B. Because of the interest factor, an annuitant is assured of receiving back more than he or she paid in. C. The emphasis is on the liquidation of the fund as opposed to its growth D. The older the annuitant is when he or she receives the first annuity payment, the greater will be the amount of each payment
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This statement is true. One of the main features of a life annuity is that it provides a guaranteed income for the rest of the annuitant's life, no matter how long they live. B. This statement is also true. The annuitant is likely to receive more than they paid Show more…
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An annuity in perpetuity is one that continues forever. Such annuities are useful in setting up scholarship funds to ensure that the award continues. a. Draw a time line (as in Example 1 ) to show that to set up an annuity in perpetuity of amount $R$ per time period, the amount that must be invested now is $$ A_{p}=\frac{R}{1+i}+\frac{R}{(1+i)^{2}}+\frac{R}{(1+i)^{3}}+\cdots+\frac{R}{(1+i)^{n}}+\cdots $$ where $i$ is the interest rate per time period. b. Find the sum of the infinite series in part (a) to show that $$ A_{p}=\frac{R}{i} $$ c. How much money must be invested now at $10 \%$ per year, compounded annually, to provide an annuity in perpetuity of $\$ 5000$ per year? The first payment is due in 1 year. d. How much money must be invested now at $8 \%$ per year, compounded quarterly, to provide an annuity in perpetuity of $\$ 3000$ per year? The first payment is due in 1 year.
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Multiple Choice What is annuity due Question options: A a series that starts at the end of the first period and increases by constant amount thereafter B a series that starts at the end of the first period and increases by constant percentage thereafter C a series that starts at the end of the first period and remains constant thereafter D a series that starts now and increases by constant amount thereafter E a series that starts now and remains constant thereafter
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