Given the following bond details:

$$ Face value: $$1,000$

$$ Coupon rate: $4\mathrm{.}5\%$ semi$-$annual

$$ Price at time t: $$1050$

$$ Price at time t$+1($six months later$)$: $$1040$

$$ Coupon payment received at t$+1$: $$45$

a$)$ Calculate the gross realized return for this bond from t to t$+1.$

b$)$ Determine the net realized return if the financing cost is $0\mathrm{.}2\%$ for the period.