A $7-$year $5\mathrm{.}5\%$ coupon $($annual$)$ bond was just issued with a face value of $$1,000$ and a yield to maturity of $4\%.$

If interest rates remain constant, by how much will the price change between now and $4$ years from now?

It will decrease by $$35\mathrm{.}58$

It will increase by $$35\mathrm{.}58$

It will decrease by $$48\mathrm{.}40$

It will increase by $$48\mathrm{.}40$