Compound Interest I: Banks compound interest on savings continuously, meaning that the

Chapter 7, Problem 7

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Compound Interest I: Banks compound interest on savings continuously, meaning that the instant the interest is earned, it also starts to earn interest. So the instantaneous rate at which the money in your account changes is directly proportional to the size of your account. As a result, your money, M, increases at a rate proportional to the amount of money in the account (Figure 7-2e), where M is in dollars, t is in years, and k is a proportionality constant. Figure 7-2e Based on what you have learned so far in calculus, determine how M varies with t. To find the value of k for a particular savings account, use the fact that if $100 is invested at an interest rate of 7% per year, then M is increasing at a rate of $7 per year at the instant M = 100. Once you have found a function that expresses M in terms of t, investigate the effects of keeping various amounts in the account for various times at various interestrates. For instance, which option gives youmore money in the long run: investing twice theamount of money, leaving the money twice aslong, or finding an interest rate twice as high?