Which annuity promises benefits that continue for life but...

Which annuity promises benefits that continue for life, but expires without value at the annuitant's death? A. A temporary annuity B. An annuity certain C. A life annuity with period certain D. A straight life annuity

An Annuity That Lasts Forever 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 one 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 one year.