A $4-$year TIPS bond has an annual coupon rate of $4$ percent and a starting face value of $$1,000.$ The actual inflation rate turned out to be $3$ percent every year for each of the $4$ years. What will be the face value of the bond at the end of Year $4?$

$$1,225$

$$1,000$

$$1,200$

$$1,126$

$$1,030$