Problem 6a: Betty and Bob have a philanthropic idea. Interest rates are 15% compound annually. They have $1,000 in an account earning that rate. At some time in per annum the future they wish to purchase a perpetuity that pays $1000 at the end of every 12 months, based on the above interest rate, to The National Charity Organization. How long must they wait; that is how long will it take for the interest bearing account to grow to an amount which will pay for the perpetuity? 6b: Generalize your results. Ifi is the rate per period and P is the principal and payment per period then find T, the time necessary to purchase the perpetuity. Express T as a function of i and P or as a function of one of the variables if that is possible. 6c: Make a table of T versus i for various rates per annum compounded annually. Make a graph of T versus i based on your table. As i increases (decreases) does T increase or decrease