A sequence of annual scholarship payments is structured so that a student receives \$6{,}000 at the beginning of the first year and then receives payments that decrease by 12\% each subsequent year in perpetuity.
(a) Let P denote the present value of all future scholarship payments, discounted at an annual effective interest rate of 4\%. Express P as an infinite series in which the first non-zero term is written explicitly.
(b) Evaluate P exactly. Give your answer in dollars.
a. Part (a)
b. Part (b)