Consider a bond to be paid back in $5$ yearly payments plus a balloon payment of

size $$50,000.$ Payment $2($as in$,$ the payment in year $2)$ is $10\%$ higher than payment

$1,$ payment $3$ is the same as payment $2,$ payment $4$ is half of payment $3,$ payment $5$

is the same as payment $4.$ The face value of the bond is $$200,000.$ The size of the

balloon payment equals the sum of all interest payments over the life of the bond.

What is the bond payment in year $4?$