Which security has a higher effective annual interest rate?

a$.$ A zero$-$coupon bond selling at $$97,645$ with par value $$100,000$ maturing in $3$ months.

b$.$ A coupon bond selling at par and paying a $10\%$ coupon semiannually.

A WSJ article on $12/28/2015$ urged millennials to ditch their parents' homes and buy their own homes now. ${?}^1$ It argues: $"$if$,$ for instance, $30-$year mortgage rates rise by one percentage point a year from now and home prices rise by another $5\%,$ a monthly mortgage payment could jump by around $18\%."$ Can you verify this statement? Assume the house price is $$500,000$ and the $30-$year mortgage rate is $4\%($APR$)$ at the end of $2015.$ What's the monthly mortgage payment? If you defer the purchase to the end of $2016,$ what's the new monthly mortgage payment $($when the house price increases by $5\%$ and the $30-$year mortgage rate becomes $5\%?$