Barbie and Ken have college debt totaling $50,000.$

Because they are just starting actuarial careers and anticipate their income to increase dramatically as they pass their actuarial exams, they would like to have an arithmetically increasing loan payment schedule.

With their anticipated exam success and resulting pay increases they anticipate that they could increase their loan payments by $5,000$ each year.

They locate a loan at an annual effective rate of $7\mathrm{.}5\%$ for $5$ years with first payment $P$ and increasing by $5000$ each year.

What is $P?$