A trust fund is being set up with a single payment of $P.$ This amount is to be invested at a fixed annual interest rate of

$r.$ The fund pays out a fixed annual amount. The first payment is to be made one year after the trust fund was set up$.$

What is the largest amount which can be paid out each year if the fund is to last for ever?

Find the present and future values of a constant income stream of $$2,000$ per year over the next $10$ years, assuming

an interest rate of $r=4\%$ annually, compounded continuously.