If an IRA is a variable-rate investment for 15 years at rate r percent per year, compounded monthly, then the future value S that accumulates from an initial investment of $1000 is S = 1000 [1 +0.01-180 12 What is the rate of change of S with respect to r and what does it tell us if the interest rate is as follows? (Round your answers to two decimal places.) (a) 6% If we were to increase the rate by 1%, the future value of the investment would increase by about $ 366.28 (b) 12% If we were to increase the rate by 1%, the future value of the investment would increase by about $ x