A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be

$ $1$ comma $000$$$1,000.$

Each year after$$ that, you will receive a payment on the anniversary of the last payment that is

$2\%2\%$

larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is

$15\%15\%$

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?