A $$50,000,25-$year strip bond earns interest at the rate of $3\mathrm{.}6\%$ compounded semi$-$annually?

$($a$)$ How much would you pay for this strip bond?

$($b$)$ What would be the value of the strip bond if interest rates for $25-$year strip bonds drop $20$ basis points just after you purchase it$?$