If an IRA is a variable-rate investment for 20 years at rate r percent per year, compounded monthly, then the future value S that accumulates from an initial investment of $1500 is S = 1500[1+0.01r/12]^240 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 $
.

(b) 12%
If we were to increase the rate by 1%, the future value of the investment would increase by about $
.