After your lifetime success, you wish to bequeath a perpetuity to your favorite niece. The first payment will occur $1$ year after you die and will be equal to $$25,000.$ Each year after that, the payment will grow by $3\%$ at a constant rate. The market interest rate is $12\%$ per year.

If you die today, what is the present value of the bequest?

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