Question $3(15$ marks$)$ Following is the time$-$line of a monthly cash flow with the

interest rate is $j_{12}=6\%$ p$.$a$.$:

$($a$)$ Find the future value of the cash flow if $x=Y=$$$100.[5$ marks$]$

$($b$)$ Find the future value of the cash flow if $x=120,Y=150.[5$ marks$]$

$($c$)$ Suppose the future value of this cash flow is $$1,220.$ Fid the size of payment Y if

$x=80.[5$ marks$]$