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Problem 4-2 Present Value of a Single Payment What is the present value of a security that will pay $25,000 in 20 years if securities of equal risk pay 8.3% annually? Round your answer to the nearest cent. Problem 4-3 Interest Rate on a Single Payment Your parents will retire in 19 years. They currently have $300,000, and they think they will need $1 million at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places. Problem 4-4 Number of Periods of a Single Payment If you deposit money today in an account that pays 6.3% annual interest, how long will it take to double your money? Round your answer to the nearest whole number. years Problem 4-5 Number of Periods of an Annuity You have $43,592.29 in a brokerage account, and you plan to deposit an additional $6,500 at the end of every future year until your account totals $425,000. You expect to earn 11.9% annually on the account. How many years will it take to reach your goal? Round your answer to the nearest whole number. years 9 Problem 4-6 Future Value: Ordinary Annuity versus Annuity Due What is the future value of a 3%, 5-year ordinary annuity that pays $650 each year? Round your answer to the nearest cent. $ If this were an annuity due, what would its future value be? Round your answer to the nearest cent. $ Problem 4-7 Present and Future Value of an Uneven Cash Flow Stream An investment will pay $200 at the end of each of the next 3 years, $300 at the end of Year 4, $600 at the end of Year 5, and $800 at the end of Year 6. If other investments of equal risk earn 10% annually, what is its present value? Round your answer to the nearest cent. $ What is its future value? Round your answer to the nearest cent. $ Problem 4-8 Annuity Payment and EAR You want to buy a car, and a local bank will lend you $10,000. The loan would be fully amortized over 4 years (48 months), and the nominal interest rate would be 12%, with interest paid monthly. What is the monthly loan payment? Round your answer to the nearest cent. $ What is the loan's EFF%? Round your answer to two decimal places. % 10 Problem 4-9 Present and Future Values of Single Cash Flows for Different Periods Find the following values, using the equations, and then work the problems using a financial calculator to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.) 1. An initial $500 compounded for 1 year at 3.3%. Round your answers to the nearest cent. $ 2. An initial $500 compounded for 2 years at 3.3%. Round your answers to the nearest cent. $ 3. The present value of $500 due in 1 year at a discount rate of 3.3%. Round your answers to the nearest cent. $ 4. The present value of $500 due in 2 years at a discount rate of 3.3%. Round your answers to the nearest cent. $ 11 Problem 4-10 Present and Future Values of Single Cash Flows for Different Interest Rates Use both the TVM equations and a financial calculator to find the following values. Round your answers to the nearest cent. (Hint: Using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.) 1. An initial $500 compounded for 10 years at 7.9 percent. $ 2. An initial $500 compounded for 10 years at 15.8 percent. $ 3. The present value of $500 due in 10 years at a 7.9 percent discount rate. $ 4. The present value of $500 due in 10 years at a 15.8 percent discount rate. $ 12 5. Problem 4-11 Time for a Lump Sum to Double How long will it take $200 to double if it is deposited and earns the following rates? Round your answers up to the next highest year. [Notes: (1) This problem cannot be solved exactly with some financial calculators. For example, if you enter PV = -200, PMT = 0, FV = 400, and I = 7 in an HP-12C and then press the N key, you will get 11 years. The correct answer is 10.2448 years, which rounds to 10, but the calculator rounds up. However, the HP10BII gives the exact answer; (2) If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer.] 1. 4.9%. year(s) 2. 9.6%. year(s) 3. 19.4%. year(s) 4. 100%. year(s) 13 Problem 4-12 Future Value of an Annuity Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1; that is, they are ordinary annuities. Round your answers to the nearest cent. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.) 1. $400 per year for 10 years at 6%. $ 2. $200 per year for 5 years at 3%. $ 3. $400 per year for 5 years at 0%. $ Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due. 4. $400 per year for 10 years at 6%. $ 5. $200 per year for 5 years at 3%. $ 6. $400 per year for 5 years at 0%. $ 14 Problem 4-13 Present Value of an Annuity Find the present value of the following ordinary annuities. Round your answers to the nearest cent. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.) 1. $800 per year for 10 years at 14%. $ 2. $400 per year for 5 years at 7%. $ 3. $800 per year for 5 years at 0%. $ Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due. 4. $800 per year for 10 years at 14%. $ 5. $400 per year for 5 years at 7%. $ 6. $800 per year for 5 years at 0%. $ 15 Problem 4-14 Uneven Cash Flow Stream 1. Find the present values of the following cash flow streams. The appropriate interest rate is 14%. Round your answers to the nearest cent. (Hint: It is fairly easy to work this problem dealing with the individual cash flows. However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows such as the ones in this problem. This will take a little time, but the investment will pay huge dividends throughout the course. Note that, when working with the calculator's cash flow register, you must enter CF0 = 0. Note also that it is quite easy to work the problem with Excel, using procedures described in the Chapter 4 Tool Kit.) Year Cash Stream A Cash Stream B 1 $100 $300 2 400 400 3 400 400 4 400 400 5 300 100 2. Stream A $ Stream B $ What is the value of each cash flow stream at a 0% interest rate? Round your answers to the nearest cent. Stream A $ Stream B $ 16 Problem 4-15 Effective Rate of Interest Find the interest rate (or rates of return) for each of the following situations. Round your answers to two decimal places. 1. You borrow $650 and promise to pay back $715 at the end of 1 year. % You lend $650 and receive a promise to be paid $715 at the end of 1 year. % You borrow $70,000 and promise to pay back $108,328 at the end of 8 years. % You borrow $8,000 and promise to make payments of $2,444.9 at the end of each year for 4 years. % Problem 4-16 17 Future Value for Various Compounding Periods Find the amount to which $375 will grow under each of the following conditions. Round your answer to the nearest cent. 1. 11% compounded annually for 5 years $ 11% compounded semiannually for 5 years $ 11% compounded quarterly for 5 years $ 11% compounded monthly for 5 years $ Problem 4-17 Present Value for Various Compounding Periods Find the present value of $350 due in the future under each of the following conditions. Round your answers to the nearest cent. 1. 6% nominal rate, semiannual compounding, discounted back 5 years $ 6% nominal rate, quarterly compounding, discounted back 5 years $ 6% nominal rate, monthly compounding, discounted back 1 year $ 18 Problem 4-20 Amortization Schedule 1. Set up an amortization schedule for a $45,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 7%. Round your answers to the nearest cent. Enter "0" if required Year Payment Repayment Interest Repayment of Principal Balance 1 $ $ $ $ 2 $ $ $ $ 3 $ $ $ $ 4 $ $ $ $ 5 $ $ $ $ Total $ $ $ 2. How large must each annual payment be if the loan is for $90,000? Assume that the interest rate remains at 7% and that the loan is paid off over 5 years. Round your answer to the nearest cent. $ How large must each payment be if the loan is for $90,000, the interest rate is 7%, and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Round your answer to the nearest cent. $ Why are these payments not half as large as the payments on the loan in part b? -Select- Item 26 I. Because the payments are spread out over a longer time period, less interest is paid on the loan, which raises the amount of each payment. II. Because the payments are spread out over a longer time period, less interest is paid on the loan, which lowers the amount of each payment. III. Because the payments are spread out over a shorter time period, more interest is paid on the loan, which lowers the amount of each payment. IV. Because the payments are spread out over a longer time period, more interest must be paid on the loan, which raises the amount of each payment. V. Because the payments are spread out over a longer time period, more principal must be paid on the loan, which raises the amount of each payment. 19 Problem 4-21 Growth Rates Sales for Hanebury Corporation's just-ended year were $14 million. Sales were $7 million 5 years earlier. a. At what rate did sales grow? Round your answer to the nearest whole number. % Problem 4-25 Repaying a Loan While Mary Corens was a student at the University of Tennessee, she borrowed $12,000 in student loans at an annual interest rate of 7.10%. If Mary repays $1,500 per year, how long (rounded up to the nearest year) will it take her to repay the loan? Problem 4-27 Present Value of a Perpetuity What is the present value of a perpetuity of $600 per year if the appropriate discount rate is 9.37%? Round your answer to the nearest cent. $ If interest rates in general were to double and the appropriate discount rate rose to 18.74%, what would its present value be? Round your answer to the nearest cent. $

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