Suppose you just bought an annuity with $10$ annual payments of $$16,500$ at a

discount rate of $13\mathrm{.}75$ percent per year.

a$.$ What is the value of the investment at the current interest rate of $13\mathrm{.}75$

percent?

Note: Do not round intermediate calculations and round your answer to

$2$ decimal places, e$.$g$.,32\mathrm{.}16.$

b$.$ What happens to the value of your investment if interest rates suddenly

drop to $8\mathrm{.}75$ percent?

Note: Do not round intermediate calculations and round your answer to

$2$ decimal places, e$.$g$.,32\mathrm{.}16.$

c$.$ What happens to the value of your investment if interest rates suddenly

rise to $18\mathrm{.}75$ percent?

Note: Do not round intermediate calculations and round your answer to

$2$ decimal places, e$.$g$.,32\mathrm{.}16.$