A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $ $4$ comma $000.$ Each year after$$ that, you will receive a payment on the anniversary of the last payment that is nbsp $8\%$ larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is $10\%$ 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?