A U$.$S$.$ Treasury bond will pay a lump sum of $$1,000$ exactly $3$ years from today. The nominal interest rate is $6\%,$ semiannual compounding. Which of the following statements is CORRECT?

a$.$ The periodic interest rate is greater than $3\%.$

b$.$ The PV of the $$1,000$ lump sum has a greater present value than the PV of a $3-$year, $$333\mathrm{.}33$ ordinary annuity.

c$.$ The present value would be greater if the lump sum were discounted back for more periods.

d$.$ The present value of the $$1,000$ would be larger if interest were compounded monthly rather than semiannually.

e$.$ The periodic rate is equal to $3\%.$