134 Chapter 3 Compound Interest
C. Solving for Time
- 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? - 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? - 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
- Find the nominal rate compounded daily that would be equivalent to an effective rate of 8.77%.
- 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? - 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? - 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
- 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? - 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?