I have this question above and would like to know how the calculations for the macaulay's duration in order to anwers the questions.

Question: you are considering three bonds. Bond A is a zero$-$coupon bond that pays $$1,000$ at maturity. Bond B has an $8\%$ coupon and pays $$80$ once per year. Bond C has a $10\%$

coupon and pays a $$50$ coupon twice per year. All three bonds mature in $3$ years and

are priced to yield $8\%$ to maturity.

$($a$)$ Calculate the modified duration for each bond.

$($b$)$ Which bond is most sensitive to interest rate changes? What will be the impact

of a $10-$basis point increase in interest rate on the prices of the three bonds?

$($c$)$ Which bond will you buy if you expected the interest rates to go up$?$