Compute the present value for each of the following amounts:

a$.$ $$200,000$ received $5$ years hence if the annual interest rate is:

$1.8\%$ compounded annually

$2.8\%$ compounded semiannually.

b$.$ $$5,000$ received at the end of each year for the next ten years discounted at $10\%$ compounded annually.

c$.$ $$1,000$ received at the end of each six months for the next $10$ years if the interest rate is $10\%$ per year compounded semiannually.