Which of the following is NOT true?

a) Macaulay duration is always longer than Modified Duration (if interest rates>0)

b)When interest rates change, the resulting change in the bond price can be calculated by multiplying the Modified duration by the change in the interest rate and the price of the bond

c)all of these are correct

d)Macaulay duration equals time to maturity for zero coupon bonds

e)When interest rates change, the resulting change in the bond price can be calculated by multiplying the Macaulay duration by the change in the interest rate and the price of the bond