You plan to retire at age $40$ after a highly successful but short career. You would like to accu enough money by age $40$ to withdraw $$225,000$ per year for $40$ years. You plan to pay into your $15$ equal installments beginning when you are $25$ and ending when you are $39.$ Your accoun interest of $12$ percent per year.

Required:

How much do you need to accumulate in your account by the time you retire?

How much do you need to pay into your account in each of the $15$ equal installments?

Is this a future$-$value problem or a present$-$value problem? Explain.