Duration, convexity and the size of the leftover

A 10-year zero-coupon bond with face value 100 is priced at an annually compounded yield $y$, so $P(y) = 100(1+y)^{-10}$. The yield is $5\%$ and jumps to $6\%$.

Estimate the new price with a first-order and then a second-order Taylor expansion in $y$. Without computing the exact price, give a bound on the error of the second-order estimate and say whether it is too high or too low. Then check against the exact price.