3. [10 pts] In this problem, we'll recall a few basic concepts from finance. First, if some prin- cipal investment P is invested for t years at interest rate r, then if the interest is compounded annually, the return is R = P(1+r). If the interest is compounded twice a year (and at even intervals) the return is R = P(1+). That is, the interest rate is cut in half over each period, but there are twice as many periods. More generally, if the interest is compounded n times a year (again, at evenly spaced intervals) the return becomes R P(1+). Recalling that limo (1+)"=e, we see that continuously compounded interest will yield a return governed by R = Pert. (lim (1+) = lim ((1+)) = e.) = a. Write a MATLAB script M-file that computes the return after 5 years for an investment of 100 dollars at 5% (r = .05) under three different plans: compounding annually, compounding monthly, and compounding continuously. Include both the M-file and a diary session of its implementation. b. Write a MATLAB function M-file that takes as input (in the function statement) t years, interest rate r, and principal P, and returns values through the function statement from the same three plans as described in (a). Include both the M-file and a diary session of its implementation.