A middle age couple has made an agreement with Landscape Forever Company, a gravesite landscaping and maintenance firm. The agreement states that the company will provide deluxe maintenance for the couples selected gravesite forever for an annual fee of $$1000.$ To arrange payment the couple has set up a variable rate perpetual trust fund with their bank. The bank guarantees that the trust fund will earn a minimum of $5\%$ per year. Assume that the services of Landscape Forever will not be needed until one of them die, and that they live until the age of $100.$

What is the minimum amount of money that the couple would have to deposit into the trust fund

$($ANSWER PART I is $20000($P$/$F$,5\%,49)$

PART II

Suppose that the couple made this minimum deposit at the age of $50,$ and suppose that the that interest rate changes as follows.

Age $50-545\%$

Age $55-6410\%$

Age $65-7415\%$

Age $75-8420\%$

What is the largest sum of money they can withdraw at age $84$ and still have money for the landscape?