Alex is planning for retir.. and is considering two annuity options:Annuity A$,$ which pays RM$1,500$ every quarter, and Annuity B$,$ which pays RM$6,000$ annually. Both annuities offer a fixed interest rate of $4\%$ per annum, compounded quarterly. Alex intends to invest in one of these annuities for a period of $10$ years$\mathrm{.}1.$ Calculate the future value of both Annuity A and Annuity B after $10$ years$\mathrm{.}2.$ Analyze and explain the impact of the payment frequency on the future value of the annuities, considering the quarterly compounding of interest$\mathrm{.}3.$ If Alex decides to extend theinvestment period to $15$ years, recalculate the future value for both annuities and discuss how the extended time horizon affects the overall returns.