A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $$4,000.$ Each year after that, you will receive a payment on the anniversary of the last payment that is $2\%$ larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is $12\%$ per year.

a$.$ What is today's value of the bequest?

b$.$ What is the value of the bequest immediately after the first payment is made?

a$.$ What is today's value of the bequest?

Today's value of the bequest is $ $($Round to the nearest cent.$)$