Suppose there is a bond with a $10\%$ yield, $5\%$ coupon rate, $$1,000$ face value, and $1\mathrm{.}5-$year maturity.

Compute the duration, convexity measure, duration$-$implied prices, and duration$-$and$-$convexity implied prices

for this bond. $(30$ points.$)$

$($Note: I recommend calculating the true duration and convexity, then using numerical derivatives to double$-$

check that your duration and convexity estimates are correct.$)$

Duration:

Convexity measure: