Problems Easy Problems 5-1 1-8 5-2 5-3 FUTURE VALUE If you deposit $2,000 in a bank account that pays 6% interest annually, how much will be in your account after 5 years? PRESENT VALUE What is the present value of a security that will pay $29,000 in 20 years if securities of equal risk pay 5% annually? FINDING THE REQUIRED INTEREST RATE Your parents will retire in 19 years. They currently have $350,000 saved, and they think they will need $800,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? 5-4 TIME FOR A LUMP SUM TO DOUBLE If you deposit money today in an account that 4% annual interest, how long will it take to double your money? pays 5-5 5-6 5-7 5-8 TIME TO REACH A FINANCIAL GOAL You have $33,556.25 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $220,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal? FUTURE VALUE: ANNUITY VERSUS ANNUITY DUE What's the future value of a 5%, 5-year ordinary annuity that pays $800 each year? If this was an annuity due, what would its future value be? PRESENT AND FUTURE VALUES OF A CASH FLOW STREAM An investment will pay $150 at the end of each of the next 3 years, $250 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 11% annually, what is its present value? Its future value? LOAN AMORTIZATION AND EAR You want to buy a car, and a local bank will lend you $40,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 8% with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR? 5-12 someone made this statement: "Sales growth of 100% in 5 years; so dividing 100% by year." Is the statement correct? EFFECTIVE RATE OF INTEREST Find the interest a. You borrow $720 and promise to pay back $79 b. You lend $720 and the borrower promises to c. You borrow $65,000 and promise to pay back d. You borrow $15,000 and promise to make pay for 5 years. 5-13 TIME FOR A LUMP SUM TO DOUBLE How long following rates? Compounding occurs once a y a. 6% b. 13% c. 21% d. 100% 5-14 FUTURE VALUE OF AN ANNUITY Find the fir Compounding occurs once a year. 5-15 a. $500 per year for 8 years at 14% b. $250 per year for 4 years at 7% c. $700 per year for 4 years at 0% d. Rework parts a, b, and c assuming they PRESENT VALUE OF AN ANNUITY Find the Discounting occurs once a year. a. $600 per year for 12 years at 8% b. $300 per year for 6 years at 4% c. $500 per year for 6 years at 0% d. Rework parts a, b, and c assuming the 5-16 PRESENT VALUE OF A PERPETUITY Wha interest rate is 5%? If interest rates doubl on that same day. The difference between the PV of costs and the an the savings account must be made up by the father's deposits, so find the six equal payments that will compound to the required amount.) prehensive/Spreadsheet Problem 5-41 TIME VALUE OF MONEY Answer the following questions: a. Assuming a rate of 10% annually, find the FV of $1,000 after 5 years. b. What is the investment's FV at rates of 0%, 5%, and 20% after 0, 1, 2, 3, 4, and 5 years? c. Find the PV of $1,000 due in 5 years if the discount rate is 10%. d. What is the rate of return on a security that costs $1,000 and returns $2,000 after 5 years? e. Suppose California's population is 36.5 million people and its population is expected to grow by 2% annually. How long will it take for the population to double? f. Find the PV of an ordinary annuity that pays $1,000 each of the next 5 years if the interest rate is 15%. What is the annuity's FV? g. How will the PV and FV of the annuity in part f change if it is an annuity due? h. What will the FV and the PV be for $1,000 due in 5 years if the interest rate is 10%, semiannual compounding? i. What will the annual payments be for an ordinary annuity for 10 years with a PV of $1,000 if the interest rate is 8%? What will the payments be if this is an annuity due?