46 THE BASICS OF INTEREST THEORY Practice Problems Problem 6.1 If $4,000 is invested at an annual rate of 6.0% compounded annually, what will be the final value of the investment after 10 years? Problem 6.2 Jack has deposited $1,000 into a savings account. He wants to withdraw it when it has grown to $2,000. If the interest rate is 4% annual interest compounded annually, how long will he have to wait? Problem 6.3 At a certain rate of compound interest, $250 deposited on July 1, 2005 has to accumulate to $275 on January 1, 2006. Assuming the interest rate does not change and there are no subsequent deposits, find the account balance on January 1, 2008. Problem 6.4 You want to triple your money in 25 years. What is the annual compound interest rate necessary to achieve this? Problem 6.5 You invest some money in an account earning 6% annual compound interest. How long will it take to quadruple your account balance? (Express your answer in years to two decimal places.) Problem 6.6 An amount of money is invested for one year at a rate of interest of 3% per quarter. Let D(k) be the difference between the amount of interest earned on a compound interest basis, and on a simple interest basis for quarter k, where k = 1,2,3,4. Find the ratio of D(4) to D(3)