You bought a $4-$year, $7\%$ coupon, $$1,000$ face value bond a year ago when it had a YTM of $3\%.$ How much did you pay? What is the bond$$s duration? A year later, with three years until maturity the yield to maturity has increased to $8\%.$ What is the new price of the bond and what return would you earn on your investment if you sold the bond after exactly one year?