CHAPTER 5: THE VALUE OF MONEY

CHAPTER 5: THE VALUE OF MONEY Multiple Choice: True/False Starting to invest early for retirement increases the benefits of compound interest a True b False ANSWER: True Starting to invest early for retirement reduces the benefits of compound interest a True b False ANSWER: False A time line is meaningful even if all cash flows not occur annually a True b False ANSWER: True A time line is not meaningful unless all cash flows occur annually a True b False ANSWER: False Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly a True b False ANSWER: True Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly a True b False ANSWER: False Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods a True b False ANSWER: True Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods a True b False ANSWER: False Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts a True b False ANSWER: True 10 Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts a True b False ANSWER: False 11 If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series a True b False ANSWER: False 12 If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series a True b False ANSWER: True 13 Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value a True b False ANSWER: True 14 Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value a True b False ANSWER: False 15 If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate a True b False ANSWER: False 16 If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate a True b False ANSWER: True 17 The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time and (2) the greater the present value of a given lump sum to be received at some future date a True b False ANSWER: False 18 The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time and (2) the smaller the present value of a given lump sum to be received at some future date a True b False ANSWER: True 19 Suppose Sally Smith plans to invest $1,000 She can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12% After 11 years, the compounded value of Security B should be more than twice the compounded value of Security A (Ignore risk, and assume that compounding occurs annually.) a True b False ANSWER: True RATIONALE: Work out the numbers with a calculator: Years 11 FVB > × FVA, so TRUE 20 Suppose Randy Jones plans to invest $1,000 He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12% After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A (Ignore risk, and assume that compounding occurs annually.) a True b False ANSWER: False RATIONALE: Work out the numbers with a calculator: Years 11 FVB > × FVA, so FALSE 21 The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant a True b False ANSWER: True 22 The present value of a future sum increases as either the discount rate or the number of periods per year increases, other things held constant a True b False ANSWER: False 23 All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases a True b False ANSWER: True RATIONALE: One could make up an example and see that the statement is true Alternatively, one could simply recognize that the PV of an annuity declines as the discount rate increases and recognize that more frequent compounding increases the effective rate 24 All other things held constant, the present value of a given annual annuity increases as the number of periods per year increases a True b False ANSWER: False RATIONALE: One could make up an example and see that the statement is false Alternatively, one could simply recognize that the PV of an annuity declines as the discount rate increases and recognize that more frequent compounding increases the effective rate 25 If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year a True b False ANSWER: True 26 If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year a True b False ANSWER: False 27 As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the nominal rate on the deposit (or loan) a True b False ANSWER: True 28 As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or less than the nominal rate on the deposit (or loan) a True b False ANSWER: False 29 When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment’s percentage declines in the loan’s later years a True b False ANSWER: False 30 When a loan is amortized, a relatively low percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment’s percentage increases in the loan’s later years a True b False ANSWER: True 31 The payment made each period on an amortized loan is constant, and it consists of some interest and some principal The closer we are to the end of the loan’s life, the greater the percentage of the payment that will be a repayment of principal a True b False ANSWER: True 32 The payment made each period on an amortized loan is constant, and it consists of some interest and some principal The closer we are to the end of the loan’s life, the smaller the percentage of the payment that will be a repayment of principal a True b False ANSWER: False 33 Midway through the life of an amortized loan, the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal This is true regardless of the original life of the loan or the interest rate on the loan a True b False ANSWER: False RATIONALE: There is no reason to think that this statement would always be true The portion of the payment representing interest declines, while the portion representing principal repayment increases Therefore, the statement is false We could also work out some numbers to prove this point Here’s an example for a 3-year loan at a 10% and a 41.45% annual interest rate The interest component is not equal to the principal repayment component except at the high interest rate Original loan $1,000 Original loan $1,000 Rate 10% Rate 41.45% Life Life Payment Beg $402.11 End Payment Beg $640.98 End Balance Interest Principal Bal Balance Interest Principal Bal $1,000.00 $100.00 $302.11 $697.89 $1,000.00 $414.50 $226.48 $773.52 $ 697.89 $ 69.79 $332.33 $365.56 $ 773.52 $320.62 $320.36 $453.15 $ 365.56 $ 36.56 $365.56 $ 0.00 $ 453.15 $187.83 $453.15 $ 0.00 34 Midway through the life of an amortized loan, the percentage of the payment that represents interest could be equal to, less than, or greater than to the percentage that represents repayment of principal The proportions depend on the original life of the loan and the interest rate a True b False ANSWER: True RATIONALE: This statement is true The portion of the payment representing interest declines, while the portion representing principal repayment increases The interest portion could be equal to, greater than, or less than the principal portion We can work out some numbers to prove this point Here’s an example for a 3-year loan at a 10% and a 41.45% annual interest rate The interest component is less than the principal at 10%, equal at about 41.45%, and greater at rates above 41.45% Original loan $1,000 Original loan $1,000 Rate 10% Rate 41.45% Life Life Payment $402.11 Payment $640.98 Beg End Beg End Balance Interest Principal Bal Balance Interest Principal Bal $1,000.00 $100.00 $302.11 $697.89 $1,000.00 $414.50 $226.48 $773.52 $ 697.89 $ 69.79 $332.33 $365.56 $ 773.52 $320.62 $320.36 $453.15 $ 365.56 $ 36.56 $365.56 $ 0.00 $ 453.15 $187.83 $453.15 $ 0.00 Multiple Choice: Conceptual Please note that some of the answer choices, or answers that are very close, are used in different questions This has caused us no difficulties, but please take this into account when you make up exams 35 Which of the following statements is CORRECT? a A time line is not meaningful unless all cash flows occur annually b Time lines are useful for visualizing complex problems prior to doing actual calculations c Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly d Time lines cannot be constructed for annuities where the payments occur at the beginning of the periods e Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts ANSWER: b 36 Which of the following statements is CORRECT? a A time line is not meaningful unless all cash flows occur annually b Time lines are not useful for visualizing complex problems prior to doing actual calculations c Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly d Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods e Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts ANSWER: d 37 Which of the following statements is CORRECT? a A time line is not meaningful unless all cash flows occur annually b Time lines are not useful for visualizing complex problems prior to doing actual calculations c Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly d Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities e Time lines cannot be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity ANSWER: c 38 Which of the following statements is CORRECT? a A time line is not meaningful unless all cash flows occur annually b Time lines are not useful for visualizing complex problems prior to doing actual calculations c Time lines cannot be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly d Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities e Time lines can be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity ANSWER: e 39 You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows Which of the following would lower the calculated value of the investment? a The cash flows are in the form of a deferred annuity, and they total to $100,000 You learn that the annuity lasts for only rather than 10 years, hence that each payment is for $20,000 rather than for $10,000 b The discount rate increases c The riskiness of the investment’s cash flows decreases d The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years e The discount rate decreases ANSWER: b 40 You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows Which of the following would increase the calculated value of the investment? a The cash flows are in the form of a deferred annuity, and they total to $100,000 You learn that the annuity lasts for 10 years rather than years, hence that each payment is for $10,000 rather than for $20,000 b The discount rate decreases c The riskiness of the investment’s cash flows increases d The total amount of cash flows remains the same, but more of the cash flows are received in the later years and less are received in the earlier years e The discount rate increases ANSWER: b 41 Which of the following statements is CORRECT? a The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods b If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity c The cash flows for an annuity due must all occur at the ends of the periods d The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month e If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity ANSWER: d 42 Which of the following statements is CORRECT? a The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods b If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity c The cash flows for an annuity due must all occur at the beginning of the periods d The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month e If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity ANSWER: c 43 Your bank account pays a 6% nominal rate of interest The interest is compounded quarterly Which of the following statements is CORRECT? a The periodic rate of interest is 1.5% and the effective rate of interest is 3% a $ 9,699 b $10,210 c $10,747 d $11,284 e $11,849 ANSWER: c RATIONALE: I/YR = 12.0% 01234 CFs: $0 $1,500 $3,000 $4,500 $6,000 PV of CFs: $0 $1,339 $2,392 $3,203 $3,813 PV = $10,747 Found using the Excel NPV function PV = $10,747 Found by summing individual PVs PV = $10,747 Found using the calculator NPV key 126 What is the present value of the following cash flow stream at a rate of 8.0%? a $7,917 b $8,333 c $8,772 d $9,233 e $9,695 ANSWER: d RATIONALE: I/YR = 8.0% 0123 CFs: $750 $2,450 $3,175 $4,400 PV of CFs: $750 $2,269 $2,722 $3,493 PV = $9,233 Found by summing individual PVs Found with a calculator or Excel to automate the process With a PV = $9,233 calculator, input the cash flows and I into the cash flow register, then press the NPV key 127 You sold a car and accepted a note with the following cash flow stream as your payment What was the effective price you received for the car assuming an interest rate of 6.0%? a $5,987 b $6,286 c $6,600 d $6,930 e $7,277 ANSWER: a RATIONALE: I/YR = 6.0% 01234 CFs: $0 $1,000 $2,000 $2,000 $2,000 PV of CFs: $0 $ 943 $1,780 $1,679 $1,584 PV = $5,987 Found using the Excel NPV function PV = $5,987 Found by summing individual PVs PV = $5,987 Found using the calculator NPV key 128 At a rate of 6.5%, what is the future value of the following cash flow stream? a $526.01 b $553.69 c $582.83 d $613.51 e $645.80 ANSWER: e RATIONALE: I/YR = 6.5% 01234 CFs: $0 $75 $225 $0 $300 PV of CFs: $0 $91 $255 $0 $300 $300 FV = $645.80 Found by summing individual FVs FV = $645.80 Found with the NFV key in some calculators FV = $645.80 Found with a calculator by first finding the PV of the stream, then finding the FV of that PV PV of the stream: FV of the PV: $501.99 $645.80 129 Your father paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next years, then an additional lump sum payment of $10,000 at the end of the 5th year What is the expected rate of return on this investment? a 6.77% b 7.13% c 7.50% d 7.88% e 8.27% ANSWER: c RATIONALE: I/YR 7.50% I is the discount rate that causes the PV of the inflows to equal the initial negative CF, and is found with Excel’s IRR function or by inputting the CFs into a calculator and pressing the IRR key 130 You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year What rate of return would you earn if you bought this asset? a 4.93% b 5.19% c 5.46% d 5.75% e 6.05% ANSWER: e RATIONALE: CFs: I/YR 6.05% I is the discount rate that causes the PV of the positive inflows to equal the initial negative CF I can be found using Excel’s IRR function or by inputting the CFs into a calculator and pressing the IRR key 131 What’s the future value of $1,500 after years if the appropriate interest rate is 6%, compounded semiannually? a $1,819 b $1,915 c $2,016 d $2,117 e $2,223 ANSWER: c RATIONALE: 132 What’s the present value of $4,500 discounted back years if the appropriate interest rate is 4.5%, compounded semiannually? a $3,089 b $3,251 c $3,422 d $3,602 e $3,782 ANSWER: d RATIONALE: 133 What’s the future value of $1,200 after years if the appropriate interest rate is 6%, compounded monthly? a $1,537.69 b $1,618.62 c $1,699.55 d $1,784.53 e $1,873.76 ANSWER: b RATIONALE: 134 What’s the present value of $1,525 discounted back years if the appropriate interest rate is 6%, compounded monthly? a $ 969 b $1,020 c $1,074 d $1,131 e $1,187 ANSWER: RATIONALE: 135 Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements If the APR is stated to be 18.00%, with interest paid monthly, what is the card’s EFF%? a 18.58% b 19.56% c 20.54% d 21.57% e 22.65% ANSWER: b RATIONALE: APR = Nominal rate 18.00% Periods/yr 12 EFF% = (1 + (rNOM/N))N − = 19.56% 136 Riverside Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly The loan (principal plus interest) must be repaid at the end of the year Midwest Bank also offers to lend you the $50,000, but it will charge an annual rate of 7.0%, with no interest due until the end of the year How much higher or lower is the effective annual rate charged by Midwest versus the rate charged by Riverside? a 0.52% b 0.44% c 0.36% d 0.30% e 0.24% ANSWER: d RATIONALE: This problem can be worked using the interest conversion feature of a calculator or Excel It could also be worked using the conversion formula We used the conversion formula Nominal rate, Riverside 6.5% Nominal rate, Midwest 7.0% Periods/yr, Riverside 12 Periods/yr, Midwest EFF% Riverside = (1 + (rNOM/N))N − = 6.70% EFF% Midwest 7.00% Difference 0.30% 137 Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year What is the effective annual rate on the loan? a 8.24% b 8.45% c 8.66% d 8.88% e 9.10% ANSWER: a RATIONALE: Nominal I/YR 8.00% Periods/yr EFF% = (1 + (rNOM/N))N − = 8.24% You could also find the EFF% as follows: Interest paid each quarter = Loan × Rate/4 = Qtrly PMT = $200.00 Then find the IRR as a quarterly rate and convert to an annual rate This procedure is obviously longer 01234 CFs: 10,000.00 10,000.00 −200.00 −200.00 −200.00 −200.00 −200.00 −200.00 −200.00 −10,000.00 −10,200.00 IRR (quarterly) = 2.00% Annual effective rate = 8.24% vs nominal rate = 8.00% 138 Suppose a bank offers to lend you $10,000 for year on a loan contract that calls for you to make interest payments of $250.00 at the end of each quarter and then pay off the principal amount at the end of the year What is the effective annual rate on the loan? a 8.46% b 8.90% c 9.37% d 9.86% e 10.38% ANSWER: e RATIONALE: Interest payment: $250.00 01234 CFs: 10,000 10,000 −250 −250 −250 −250 −250 −250 −250 −10,000 −10,250 IRR (quarterly) = 2.50% Annual effective rate = 10.38% vs nominal rate = 10.00% 139 Charter Bank pays a 4.50% nominal rate on deposits, with monthly compounding What effective annual rate (EFF%) does the bank pay? a 3.72% b 4.13% c 4.59% d 5.05% e 5.56% ANSWER: c RATIONALE: Nominal I/YR 4.50% Periods/yr 12 Periodic rate 0.38% EFF% = (1 + (rNOM/N))N − = 4.59% 140 Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding What is the effective annual rate? a 15.27% b 16.08% c 16.88% d 17.72% e 18.61% ANSWER: b RATIONALE: Nominal I/YR = APR 15.00% Periods/yr 12 EFF% = (1 + (rNOM/N))N − = 16.08% 141 Pace Co borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month The bank uses a 360-day year How much interest would Pace have to pay in a 30-day month? a $120.83 b $126.88 c $133.22 d $139.88 e $146.87 ANSWER: a RATIONALE: Nominal I/YR 7.25% Days in month 30 Days/yr 360 Daily rate 0.020139% Amount borrowed $20,000 Interest per day $4.02778 Interest per month = Interest/day × 30 = $120.83 142 Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year How much would be in the account after months, assuming each month has 30 days? a $5,178.09 b $5,436.99 c $5,708.84 d $5,994.28 e $6,294.00 ANSWER: a RATIONALE: 143 Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in equal installments at the end of each of the next years How large would your payments be? a $3,704.02 b $3,889.23 c $4,083.69 d $4,287.87 e $4,502.26 ANSWER: a RATIONALE: 144 Suppose you are buying your first condo for $145,000, and you will make a $15,000 down payment You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month What will your monthly payments be? a $741.57 b $780.60 c $821.69 d $862.77 e $905.91 ANSWER: c RATIONALE: Years 30 N 360 Payments/year 12 Periodic rate 0.54% Nominal rate 6.50% PV $130,000 Purchase price $145,000 FV $0.00 Down payment $15,000 PMT $821.69 145 Your uncle will sell you his bicycle shop for $250,000, with “seller financing,” at a 6.0% nominal annual rate The terms of the loan would require you to make 12 equal end-of-month payments per year for years, and then make an additional final (balloon) payment of $50,000 at the end of the last month What would your equal monthly payments be? a $4,029.37 b $4,241.44 c $4,464.67 d $4,699.66 e $4,947.01 ANSWER: e RATIONALE: Monthly annuity, so interest must be calculated on a monthly basis Years Payments/year 12 N 48 Nominal rate 6.0% PV $250,000 I/period 0.5% FV $50,000 PMT $4,947.01 146 Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in equal installments at the end of each of the next years How much interest would you have to pay in the first year? a $1,200.33 b $1,263.50 c $1,330.00 d $1,400.00 e $1,470.00 ANSWER: d RATIONALE: I/YR 10.0% Years Amount borrowed $14,000 Interest in Year $1,400.00 Simply multiply the rate times the amount borrowed 147 You plan to borrow $35,000 at a 7.5% annual interest rate The terms require you to amortize the loan with equal end-of-year payments How much interest would you be paying in Year 2? a $1,994.49 b $2,099.46 c $2,209.96 d $2,326.27 e $2,442.59 ANSWER: d RATIONALE: Find the required payment: N7 I 7.5% PV $35,000 FV $0 PMT $6,608.01 Found with a calculator or Excel Amortization schedule (first years) Year Beg Balance Payment Interest Principal End Balance 35,000.00 6,608.01 2,625.00 3,983.01 31,016.99 31,016.99 6,608.01 2,326.27 4,281.74 26,735.25 148 Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business The terms require you to amortize the loan with 10 equal end-of-year payments How much interest would you be paying in Year 2? a $7,531 b $7,927 c $8,323 d $8,740 e $9,177 ANSWER: b RATIONALE: Find the required payment: N 10 I 8.5% PV $100,000 FV $0 PMT $15,241 Found with a calculator or Excel Amortization schedule (first years) Year Beg Balance Payment Interest Principal End Balance 100,000 15,241 8,500 6,741 93,259 93,259 15,241 7,927 7,314 85,945 149 You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000? Round frac nal months up a 23 b 27 c 32 d 38 e 44 ANSWER: d RATIONALE: BEGIN Mode I/YR 18.0% I/MO 1.5% Monthly annuity due, so interest must be calculated on monthly basis rNOM/12 150 You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000? a 39.60 b 44.00 c 48.40 d 53.24 e 58.57 ANSWER: b RATIONALE: I/YR 7.0% I/MO 0.583333% Monthly annuity, so interest must be calculated on monthly basis PV $0 PMT $3,000 FV $150,000 N 44.0021 151 Your child’s orthodontist offers you two alternative payment plans The first plan requires a $4,000 immediate up- front payment The second plan requires you to make monthly payments of $137.41, payable at the end of each month for years What nominal annual interest rate is built into the monthly payment plan? a 12.31% b 12.96% c 13.64% d 14.36% e 15.08% ANSWER: d RATIONALE: N 36 PV $4,000 PMT $137.41 FV $0 I/MO 1.20% Monthly annuity, so interest must be calculated on monthly basis I/YR = I/MO × 12 = 14.36% 152 Your subscription to Investing Wisely Weekly is about to expire You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy? a 7.48 b 8.80 c 10.35 d 12.18 e 14.33 ANSWER: e RATIONALE: Find N for an annuity due with the indicated terms to determine how long you must live to make the lifetime subscription worthwhile BEGIN Mode Interest rate (I/YR) 6.0% Annual cost (PMT) $85 Lifetime subscription cost (PV) $850 Number of payments made (N) 14.33 153 You agree to make 24 deposits of $500 at the beginning of each month into a bank account At the end of the 24th month, you will have $13,000 in your account If the bank compounds interest monthly, what nominal annual interest rate will you be earning? a 7.62% b 8.00% c 8.40% d 8.82% e 9.26% ANSWER: a RATIONALE: BEGIN Mode N 24 PV $0 PMT $500 FV $13,000 I/MO 0.63% I/YR 7.62% 154 You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now? a $15,234.08 b $16,035.87 c $16,837.67 d $17,679.55 e $18,563.53 ANSWER: b RATIONALE: Interest rate Periods/year 4.0% Years on Quarters Ending Quarterly rate 1.0% Deposit on Deposit Amount 1st deposit $2,500 12 $ 2,817.06 2nd deposit $5,000 5,414.28 3rd deposit $7,500 7,804.53 Total $16,035.87 155 Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly Merchants Bank offers to lend you the $50,000, but it will charge 6.0%, simple interest, with interest paid at the end of the year What’s the difference in the effective annual rates charged by the two banks? a 1.56% b 1.30% c 1.09% d 0.91% e 0.72% ANSWER: d RATIONALE: Students must understand that "simple interest with interest paid quarterly" means that the bank gets the interest at the end of each quarter, hence it can invest it, presumably at the same nominal rate This results in the same effective rate as if it were stated as "6%, quarterly compounding." Nominal rate, Farmers 5.0% Periods/yr, Farmers Nominal rate, Merchants 6.0% Periods/yr, Merchants EFF% Farmers 5.09% EFF% Merchants 6.00% Difference 0.91% 156 Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in equal installments at the end of each of the next years By how much would you reduce the amount you owe in the first year? a $2,404.91 b $2,531.49 c $2,658.06 d $2,790.96 e $2,930.51 ANSWER: b RATIONALE: Interest rate 8.5% Years Amount borrowed $15,000 Step 1: Find the PMT 3,806.49 Step 2: Find the 1st year’s interest 1,275.00 Step 3: Subtract the interest from the payment; this is repayment of principal 2,531.49 ... value of DUE is less than the future value of ORD c The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE d The present value. .. present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE b The present value of DUE exceeds the present value of ORD, while the. .. present value of ORD, while the future value of DUE is less than the future value of ORD c The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the