Chapter 12.2, Problem 70E

Level curves of a savings account Suppose you make a one-time deposit of P dollars into a savings account that earns interest at an annual rate of p% compounded continuously. The balance in the account after t years is B(P, r, t) = Pe^rt, where r = p/100 (for example, if the annual interest rate is 4%, then r = 0.04). Let the interest rate be fixed at r = 0.04

a.    With a target balance of $2000, find the set of all points (P, t) that satisfy B = 2000. This curve gives all deposits P and times t that result in a balance of $2000.

b.    Repeat part (a) with B = $500, $1000, $1500, and $2500, and draw the resulting level curves of the balance function.

c.    In general, on one level curve, if t increases, does P increase or decrease?