A bond with a face value of $$1,000$ has $16$ years until maturity, has a coupon rate of $7\mathrm{.}8\%,$ and sells for $$1,071.$

a$.$ What is the yield to maturity if interest is paid once a year?

Note: Do not round intermediate calculations. Enter your answer as a percent rounded to $4$ decimal places.

Yield to maturity

$\%$

b$.$ What is the yield to maturity if interest is paid semiannually?

Note: Do not round intermediate calculations. Enter your answer as a percent rounded to $4$ decimal places.

Yield to maturity

$\%$