Present value concept Answer each of the following questions.

a$.$ How much money would you have to invest today to accumulate $$4,800$ after $9$ years if the rate of return on your investment is $12\%?$

b$.$ What is the present value of $$4,800$ that you will receive after $9$ years if the discount rate is $12\%?$

c$.$ What would you be willing to spend today for an investment that will pay $$4,800$ in $9$ years if your opportunity cost is $12\%?$ 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 $12\%$ annual interest, worth $$4,800$ at the end of $9$ years is $($Round to the nearest cent.$)$

b$.$ The present value of $$4,800$ to be received at the end of $9$ years, if the discount rate is $12\%,$ is $ $($Round to the nearest cent.$)$

c$.$ The most you would spend today for an investment that will pay $$4,800$ in $9$ years if your opportunity cost is $12\%$ is $ $($Round to the nearest cent.$)$

If you can buy the investment for less than $$1,730\mathrm{.}88$ then your implied rate of return will be $$ than $12\%.$

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

A$.$ In parts a and $c,$$$4,800$ is the future value, FV$.$ In part b$,$ $$4,800$ is the present value, $PV.$ Therefore, parts a and $c$ have the same answer, while part $b$ has a different answer.

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

C$.$ In all three cases, the answer is $$1,730\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$.$

D$.$ In all three cases, you are solving for the present value, $PV,$ which is $$1,730\mathrm{.}93.$