Level curves of a savings account.

Suppose you make a one-time deposit of PP dollars into a savings account that earns interest at an annual rate of pp% compounded continuously.

The balance in the account after tt years is

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) = Pet 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 ? d. Sketch the Graph of B(P, 0.04, t) and its level curves. e. Which representation of the function B do you prefer: graph or level curves? f. Set B = B(P, 0.04, t). Evaluate the partial derivatives Bp and Bt. g. If you move along the vertical line P= 100 in the positive t direction, how does B change? Is this consistant with Bt computed in part (f) ? Plot t HB(100, 0.04,t). h. If you move along the horizontal line t = 10 in the positive P direction, how does B change? Is this consistant with Bp computed in part (f) ? Plot t HB(P, 0.04, 10)