Present value concept Answer each of the following questions.

a$.$ How much money would you have to invest today to accumulate $$4,500$ after $4$ years if the rate of return on your investment is $13\%?$

b$.$ What is the present value of $$4,500$ that you will receive after $4$ years if the discount rate is $13\%?$

c$.$ What would you be willing to spend today for an investment that will pay $$4,500$ in $4$ years if your opportunity cost is

$13\%?$ If you could buy the investment for less than that, what would that imply about your rate of return?

d$.$ Compare, contrast, and discuss your findings in part a through $c.$

a$.$ A single investment made today, earning $13\%$ annual interest, worth $$4,500$ at the end of $4$ years is $

$.($Round to the nearest cent.$)$

b$.$ The present value of $$4,500$ to be received at the end of $4$ years, if the discount rate is $13\%,$ is $

$($Round to the nearest cent.$)$

c$.$ The most you would spend today for an investment that will pay $$4,500$ in $4$ years if your opportunity cost is $13\%$ is $$.($Round to the nearest cent.$)$

If you can buy the investment for less than $$2,759\mathrm{.}85$ then your implied rate of return will be

than $13\%.$

d$.$ Compare, contrast, and discuss your findings in part a through c$.($Select all answers that apply.$)$

A$.$ In parts a and $c,$$$4,500$ is the future value, $FV.$ In part $b,$$$4,500$ is the present value, $PV.$ Therefore, parts a and $c$ have the same answer, while part $b$ has a different answer.

B$.$ In all three cases, the answer is $$2,759\mathrm{.}93.$ In part $a,$ it is the payment, $PMT.$ In part $b,$ it is the present value, $PV.$ In part $c,$ it is the future value, $FV.$

C$.$ The annual interest rate is also called the discount rate or the opportunity cost.

D$.$ In all three cases, you are solving for the present value, $PV,$ which is $$2,759\mathrm{.}93.$