A customer buys a $$1,000$ par Treasury Inflation Protection security with a $4\%$ coupon and a $10$ year maturity. If the inflation rate during the first year of the security$\text{'}$s life is $5\%,$ the:

Principal amount is adjusted to $$1,050$ and the coupon rate remains at $4\%$

Principal amount remains at $$1,000$ and the coupon rate is adjusted to $5\%$

Principal amount remains at $$1,000$ and the coupon rate remains at $4\%$

Principal amount is adjusted to $$1,050$ and the coupon rate is adjusted to $5\%$