The Mathematics of Money

(Darren Dugan) #1

134 Chapter 3 Compound Interest


C. Solving for Time



  1. According to his fi nancial planner, Rodney’s investment portfolio can be expected to earn an 8½% effective rate.
    Assuming this is correct, how long will it take for his portfolio’s value to grow from $259,000 to $500,000?

  2. If my savings account pays a constant 3.65% compounded daily, how long will it take for my $1,893.25 account
    balance to grow to $2,000?

  3. Use the Rule of 72 to approximate the time needed to double a sum of money at a 6.5% effective rate. Then use the
    techniques of this section to fi nd the actual time required. How good was the estimate?


D. Grab Bag



  1. Find the nominal rate compounded daily that would be equivalent to an effective rate of 8.77%.

  2. Chey’s retirement account has a balance of $797,503. Assuming that she makes no deposits or withdrawals, and that
    her account earns 6¼% compounded monthly, how long will it take for her account balance to reach $1,000,000?

  3. A wind turbine manufacturer’s sales were $18,576,950 in 2005. An investment analyst predicts that the company’s
    sales will grow at an effective rate of 18% per year. Assuming this prediction is correct, how long will it be before the
    annual sales reach $100,000,000?

  4. Jack’s investment portfolio was worth $37,500 at the start of 2004, and had grown to $65,937 by the start of 2007.
    What was the effective growth rate of his account during that time period?


E. Additional Exercises



  1. Suppose that Kimberly invests $10,000, which grows at an effective rate of 8% for 3 years. For the next 2 years the
    investment grows at an effective rate of 11%, and then for the last 5 years it grows at only 5%. Taking the entire
    10 years as a whole, what was the overall effective rate that she earned?

  2. Irakli invested $30,000 in a stock. Eight years later it was worth $75,000. In the last 3 years, the stock grew at a steady
    4% rate. What was its effective growth rate for the fi rst 5 years?

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