This problem demonstrates the dependence of the present value of an annuity on the discount rate. For an ordinary annuity consisting of $20$ annual payments of $$1,500,$ calculate the present value using an annually compounded discount rate of: $($Do not round intermediate calculations and round your final answers to $2$ decimal places.$)$

a$.5\mathrm{.}5\%$

$

b$.10\mathrm{.}5\%$

$

c$.11\mathrm{.}5\%$

$

d$.15\mathrm{.}5\%$

$

Observe that the present value decreases as you increase the discount rate. However, the present value decreases proportionately less than the increase in the discount rate.