Given a cash flow of $$200$ received at the end of year one, and a cash flow of $$400$

received at the end of year three, if interest rates are as follows: year $1=4\%$; year $2=5\%$; year $3$

$=6\%$; year $4=7\%.$

$(1)$ what is the value of the cash flows today? $($Hint: a timeline will help!$)(3$ marks$).$

$(2)$ what is the value of the cash flows at the end of year four?