Chapter 14.2, Problem 52E

Work the following applied problems. (See Example 5.)

Present Value for Continuously Compounded Interest The present value P of A dollars at an interest rate r per year compounded continuously for t years is

$P=\frac{A}{e^{rt}}=A{e}^{-rt}.$

a. Would you expect $P_A$ to be positive or negative? Find $P_A$.

b. Would you expect $P_r$ to be positive or negative? Find $P_r$.

c. Would you expect $P_t$ to be positive or negative? Find $P_t$.