You plan to make five deposits of $$1,375$ each, one every $6$ months, with the first payment being made in $6$ months. You will then make no more deposits. If the bank pays $9\mathrm{.}5\%$ nominal interest, compounded semiannually, how much will be in your account after $3$ years?

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Note: Please use at least $2$ decimal places in your answer. Also, please use $4$ decimal places throughout your calculations. This will help to mitigate any issues due to rounding.

Hint: Draw a timeline. Place the $5$ deposits on the timeline and then place a question mark $(?)$ on the timeline to designate the value you want to find, i$.$e$.$ account balance in $3$ years. This is a two$-$part problem.