You are offered one of the following two options for free. Option A includes a fixed cash flow of

$$400$ every year forever that starts right now $($t $=0)$ with the first payment at the end of this year

$($t $=1).$ Option B includes a fixed cash flow of $$420$ every year forever, but it starts a year later

$($t $=1)$ with the first payment at the end of the next year $($t $=2).$ Interest rates are at $10\%$ per

year for every maturity.

$1.$ What is the value of Option A when it starts $($at t $=0)?$

$2.$ What is the value of Option B when it starts $($at t $=1)?$

$3.$ Which one should you pick and why?