Calculate the Macaulay duration of an $8\%,$$$1,000$ par bond that matures in three years if the bond's YTM is $12\%$ and interest is paid semiannually.

a$.$ Calculate this bond's modified duration. Do not round intermediate calculations. Round your answer to two decimal places.

years

b$.$ Assuming the bond's YTM goes from $12\%$ to $10\mathrm{.}5\%,$ calculate an estimate of the price change. Do not round intermediate calculations. Round your answer to three decimal places. Use a minus sign

to enter negative value, if any.

$\%$