Level curves of a savings plan Suppose you make monthly

Chapter 12, Problem 71

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Level curves of a savings plan Suppose you make monthly deposits of P dollars into an account that earns interest at a monthly rate of p%. The balance in the account after t years is B1P, r, t2 = Pa 11 + r212t - 1 r b, where r = p>100 (for example, if the annual interest rate is 9%, then p = 9 12 = 0.75 and r = 0.0075). Let the time of investment be fixed at t = 20 years. a. With a target balance of $20,000, find the set of all points 1P, r2 that satisfy B = 20,000. This curve gives all deposits P and monthly interest rates r that result in a balance of $20,000 after 20 years. b. Repeat part (a) with B = $5000, $10,000, $15,000, and $25,000, and draw the resulting level curves of the balance function.