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 $6\%$ larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is $16\%$ 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 $$40,000.($Round to the nearest dollar.$)$

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

The value of the bequest immediately after the first payment is made is $$.($Round to the nearest dollar.$)$