Salem plans to deposit $$2200$ every $6$ months for $15$ years to save for his son's higher education. The rate of return will be $4\%$ compounded semi$-$annually for the first $5$ years and $8\%$ compounded semi$-$annually for the subsequent $10$ years. Calculate the future value of this simple annuity. a$$24089\mathrm{.}39$ b$$52782\mathrm{.}81$ c$$53454\mathrm{.}21$ d$$106237\mathrm{.}02$ e$$118293\mathrm{.}81$