Suppose you want to create a perpetual family trust fund with plan to offer $$50,000$ each year, beginning $10$ years later. Suppose you can lock in a fixed interest rate of $4\%.$ Which of the following statements is NOT correct?

Select one:

a$.$ Applying the perpetuity formula $50,\frac{000}{4}\%$ produces the present value in terms of Year $9$

b$.$ The amount needed $9$ years later is $$1,250,000$

c$.$ The amount needed today is $$878,233\mathrm{.}42$

d$.$ The amount needed $10$ years from now is $$1,250,000$