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Chapter 3EquivalenceA Factor Approach3-1If you had 1,000 now and invested it at 6%, how much would it be worth 12 years from now?SolutionF 1,000(F/P, 6%, 12) 2,012.003-2Mr. Ray deposited 200,000 in the Old and Third National Bank. If the bank pays 8% interest,how much will he have in the account at the end of 10 years?SolutionF 200,000(F/P, 8%, 10) 431,8003-3If you can earn 6% interest on your money, how much is 1,000 paid to you 12 years in the futureworth to you now?SolutionP 1,000(P/F, 6%, 12) 497.003-4Determine the value of P using the appropriate factor.F 500012345i 6%PSolutionP F(P/F, 6%, 5) 500(0.7473) 373.653-5Downtown is experiencing an explosive population growth of 10% per year. At the end of 200549

50Chapter 3 Equivalence – A Factor Approachthe population was 16,000. If the growth rate continues unabated, at the end of how many yearswill it take for the population to triple?SolutionUse i 10% to represent the growth rate.48,000 16,000(F/P, 10%, n)(F/P, 10%, n) 48,000/16,000 3.000From the 10% table n is 12Note that population would not have tripled after 11 years.3-6If the interest rate is 6% compounded quarterly, how long (number of quarters) does it take to earn 100 interest on an initial deposit of 300?Solutioni 6%/4 1½%400 300(F/P, 1½%, n)(F/P, 1½%, n) 400/300 1.333From the 1½% table n 20 quarters3-7The amount of money accumulated in five years with an initial deposit of 10,000, if the accountearned 12% compounded monthly the first three years and 15% compounded semi-annually thelast two years is closest toa.b.c.d. 18,580 19,110 19,230 1,034,285SolutionF [10,000(F/P, 1%, 36)](F/P, 7.5%, 4) 10,000(1.431)(1.075)4 19,110.563-8One thousand dollars is deposited into an account that pays interest monthly and allowed toremain in the account for three years. If the annual interest rate is 6%, the balance at the end ofthe three years is closest toa. 1,180

Chapter 3 Equivalence – A Factor Approachb.c.d.51 1,191 1,197 2,898Solutioni 6/12 ½%n (12)(3) 36nF P(1 i) 1,000(1.005)36 1,196.68or using interest tablesF 1,000(F/P, ½%, 36) 1,000(1.197) 1,197The answer is c.3-9On July 1 and September 1, Abby placed 2,000 into an account paying 3% compoundedmonthly. How much was in the account on October 1?Solutioni 3/12 ¼%F 2,000(1 .0025)3 2,000(1 .0025)1 4,020.04orF 2,000(F/P, ¼%, 3) 2,000(F/P, ¼%, 1) 4,022.003-10The Block Concrete Company borrowed 20,000 at 8% interest, compounded semi-annually, to bepaid off in one payment at the end of four years. At the end of the four years, Block made apayment of 8,000 and refinanced the remaining balance at 6% interest, compounded monthly, tobe paid at the end of two years. The amount Block owes at the end of the two years is nearest toa.b.c.d. 21,580 21,841 22,020 34,184Solutioni1 8/2 4%n1 (4)(2) 8i2 6/2 ½%F [20,000(F/P, 4%, 8) -8,000](F/P, ½%, 24) 21,841.26The answer is b.n2 (12)(2)

52Chapter 3 Equivalence – A Factor Approach3-11How much should Abigail invest in a fund that will pay 9%, compounded continuously, if shewishes to have 60,000 in the fund at the end of 10 years?Solutionr 0.09n 10P Fe-rn 60,000e-.09(10) 24,394.183-12Given :i 9%F ?Jan Feb Mar Apr MayJuneP 350Find:a) Fb) ieffSolutiona) F 350(F/P, .75%, 6) 366.10b) ieff (1 i)m - 1 (1.0075)12 - 1 9.38%3-13Five hundred dollars is deposited into an account that pays 5% interest compounded continuously.If the money remains in the account for three years the account balance is nearest toa.b.c.d. 525 578 580 598SolutionF ern 500e.05(3) 580.91The answer is c.3-14The multistate Powerball Lottery, worth 182 million, was won by a single individual who hadpurchased five tickets at 1 each. The winner was given two choices: Receive 26 payments of 7million each, with the first payment to be made now and the rest to be made at the end of each ofthe next twenty five years; or receive a single lump-sum payment now that would be equivalent to

Chapter 3 Equivalence – A Factor Approach53the 26 payments of 7 million each. If the state uses an interest rate of 4% per year, the amount ofthe lump sum payment is closest toa.b.c.d. 109,355,000 111,881,000 116,354,000 182,000,000SolutionP 7,000,000 7,000,000(P/F, 4%, 25) 116,354,000The answer is c.3-15The future worth (in year 8) of 10,000 deposited at the end of year 3, 10,000 deposited at theend of year 5, and 10,000 deposited at the end of year 8 at an interest rate of 12% per year isclosest toa.b.c.d. 32,100 39,300 41,670 46,200SolutionF 10,000(F/P, 12%, 5) 10,000(F/P, 12%, 3) 10,000 41,670The answer is c.3-16A woman deposited 10,000 into an account at her credit union. The money was left on depositfor 10 years. During the first five years the woman earned 9% interest, compounded monthly.The credit union then changed its interest policy so that the second five years the woman earned6% interest, compounded quarterly.a.b.How much money was in the account at the end of the 10 years?Calculate the rate of return that the woman received.Solutiona)at the end of 5 years:F 10,000 (F/P, ¾%, 60)* 15,660.00* i 9/12 ¾%at the end of 10 years:F 15,660(F/P, 1½%, 20)** 21,094.02 ** i 6/4 1½%b) 10,000(F/P, i, 10) 21,094.02(F/P, i, 10) 2.1094n (12)(5) 60n (4)(5) 20

54Chapter 3 Equivalence – A Factor Approachtry i 7%try i 8%(F/P, 7%, 10) 1.967(F/P, 8%, 10) 2.1597% i 8% interpolatei 7.75%3-17A young engineer wishes to buy a house but only can afford monthly payments of 500. Thirtyyear loans are available at 6% interest compounded monthly. If she can make a 5,000 downpayment, what is the price of the most expensive house that she can afford to purchase?Solutioni 6/12 ½%n (30)(12) 360P* 500(P/A, ½%, 360) 83,396.00P 83,396.00 5,000P 88,3963-18A person borrows 15,000 at an interest rate of 6%, compounded monthly to be paid off withpayments of 456.33.a.b.What is the length of the loan in years?What is the total amount that would be required at the end of the twelfth month to payoff theentire loan balance?Solutiona)P A(P/A, i%, n)15,000 456.33(P/A, ½%, n)(P/A, ½%, n) 15,000/456.33 32.871From the ½% interest table n 36 months 6 years.b) 456.33 456.33(P/A, ½%, 24) 10,752.503-19A 50,000 30-year loan with a nominal interest rate of 6% is to be repaid with payments of 299.77. The borrower wants to know how many payments, N*, he will have to make until heowes only half of the amount she borrowed initially.SolutionThe outstanding principal is equal to the present worth of the remaining payments when thepayments are discounted at the loan's effective interest rate.

Chapter 3 Equivalence – A Factor Approach55Therefore, let N' be the remaining payments.½(50,000) 299.77(P/A, ½%, N')(P/A, ½%, N') 83.397N' 108.30 108From i ½% tableSo, N* 360 - N' 252 payments3-20J.D. Homeowner has just bought a house with a 20-year, 9%, 70,000 mortgage on which he ispaying 629.81 per month.a)If J.D. sells the house after ten years, how much must he pay the bank to completely pay offthe mortgage at the time of the 120th payment?b) How much of the first 629.81 payment on the loan is interest?Solutiona)P 120th payment PW of remaining 120 payments 629.81 629.81(P/A, ¾%, 120) 49,718.46b) 70,000 0.0075 5253-21While in college Ellen received 40,000 in student loans at 8% interest. She will graduate in Juneand is expected to begin repaying the loans in either 5 or 10 equal annual payments. Compute heryearly payments for both repayment plans.Solution5 YEARSA P(A/P, i, n) 40,000(A/P, 8%, 5) 10,020.003-22Given:A 22212P 800Find: i%Solution34510 YEARSA P(A/P, i, n) 40,000(A/P, 8%, 10) 5,960.00

56Chapter 3 Equivalence – A Factor ApproachP A(P/A, i %, 5)800 222(P/A, i%, 5)(P/A, i %, 5) 800/222 3.6From the interest tables i 12%3-23How much will accumulate in an Individual Retirement Account (IRA) in 15 years if 5,000 isdeposited in the account at the end of each quarter during that time? The account earns 8%interest, compounded quarterly. What is the effective interest rate?Solutioni 8/4 2%n (4)(15) 60F 5,000 (F/A, 2%, 60) 570,255.00Effective interest rate (1 .02)4 - 1 8.24%3-24Suppose you wanted to buy a 180,000 house. You have 20,000 cash to use as the downpayment. The bank offers to loan you the remainder at 6% nominal interest. The term of the loanis 20 years. Compute your monthly loan payment.SolutionAmount of loan: 180,000 - 20,000 160,000i 6/12 ½% per month n (12)(20) 240A 160,000(A/P, ½%, 240) 1,145.60 per month3-25To offset the cost of buying a 120,000 house, James and Lexie borrowed 25,000 from theirparents at 6% nominal interest, compounded monthly. The loan from their parents is to be paidoff in five years in equal monthly payments. The couple has saved 12,500. Their total downpayment is therefore 25,000 12,500 37,500. The balance will be mortgaged at 9% nominalinterest, compounded monthly for 30 years. Find the combined monthly payment that the couplewill be making for the first five years.SolutionPayment to parents:25,000(A/P, ½%, 60) 482.50Borrowed from bank: 120,000 – 37,500 82,500

Chapter 3 Equivalence – A Factor Approach57Payment to bank82,500(A/P, ¾%, 360) 664.13Therefore, monthly payments are 482.50 664.13 1,146.633-26If 15,000 is deposited into a savings account that pays 4% interest compounded quarterly, howmuch can be withdrawn each quarter for five years?SolutionA 15,000(A/P, 1%, 20) 831.00 per quarter3-27How much will Thomas accumulate in a bank account that pays 5% annual interest compoundedquarterly if he deposits 800 at the end of each quarter for 7 years?SolutionF 800(F/A, 1.25%, 28) 25,824.003-28A consumer purchased new furniture by borrowing 1,500 using the store's credit plan whichcharges 18% compounded monthly.(a) What are the monthly payments if the loan is to be repaid in 3 years?(b) How much of the first payment is interest?(c) How much does the consumer still owe just after making the 20th payment?Solution(a) A 1,500(A/P, 1½%, 36) 54.30 per month(b) Interest payment principal interest rateInterest payment 1,500 0.015 22.50(c) P 54.30(P/A, 1½%, 16) 767.313-29A company borrowed 20,000 at 8% interest. The loan was repaid according to the followingschedule. Find X, the amount that will pay off the loan at the end of year 5.

58Chapter 3 Equivalence – A Factor ApproachYearAmount12345 4,0004,0004,0004,000XSolution20,000 4,000(P/A, 8%, 4) X(P/F, 8%, 5)6,752 X(.6806)X 6,752/.6806 9,920.663-30The local loan shark has loaned you 1,000. The interest rate you must pay is 20%, compoundedmonthly. The loan will be repaid by making 24 equal monthly payments. What is the amount ofeach monthly payment?Solutioni 20/12 1-2/3%A 1,000(A/P, 1-2/3%, 24)There is no 1-2/3% compound interest table readily available. Therefore the capital recoveryfactor must be calculated.(A/P, 1.666%, 24) [0.01666(1.01666)24]/[(1.01666)24 - 1] 0.050892A 1,000(0.050892) 50.903-31Find the uniform annual equivalent for the following cash flow diagram if i 10%. Use theappropriate gradient and uniform series lutionP1 [400(P/A, 10%, 6) - 50(P/G, 10%, 6)](P/F, 10%, 2) 1,039.45P2 [150(P/A, 10%, 4)](P/F, 10%, 8) 221.82P 1,039.45 221.82 1,261.27150150

Chapter 3 Equivalence – A Factor Approach59A 1,261.27(A/P, 10%, 12) 185.153-32You need to borrow 10,000 and the following two alternatives are available at different banks:a) pay 2,571 at the end of each year for 5 years, starting at the end of the first year (5 payments intotal.) or b) pay 207.58 at the end of each month, for 5 years, starting at the end of the firstmonth. (60 payments in total). On the basis of the interest rate being charged in each case, whichalternative should you choose?SolutionAlternative a:10,000 2,571(P/A, i, 5)(P/A, i, 5) 10,000/2,571 3.890From the interest tables, i 9% The nominal annual rate effective rate.Alternative b:10,000 207.58(P/A, i, 60)(P/A, i, 60) 10,000/ 207.58 48.174From the interest tables i .75% The nominal annual interest rate is: 12 .75 9% but theeffective interest rate is (1 0.0075)12 - 1 9.38%Therefore, choose the first alternative.3-33Using a credit card, Ben Spendthrift has just purchased a new stereo system for 975 and will bemaking payments of 45 per month. If the interest rate is 18% compounded monthly, how longwill it take to completely pay off the stereo?Solutioni 18/12 1½%975 45(P/A, 1½%, n)(P/A, 1½%, n) 975/45 21.667From the 1½% table n is between 26 and 27 months. The loan will not be completely paid offafter 26 months. Therefore the payment in the 27th month will be smaller.3-34Explain in one or two sentences why (A/P, i%, infinity) i.

60Chapter 3 Equivalence – A Factor ApproachSolutionIn order to have an infinitely long annuity (A) series, the principal (present sum P) must neverbe reduced. For this to occur, only the interest earned each period may be removed. If morethan the interest earned is removed it would decrease the original P so that less interest isavailable the next period.3-35An engineer on the verge of retirement has accumulated savings of 100,000 that are in an accountpaying 6% compounded quarterly. The engineer wishes to withdraw 6,000 each quarter. Forhow long can she withdraw the full amount?Solutioni 6/4 1½%6,000 100,000(A/P, 1½%, n)(A/P, 1½%, n) 0.0600From the 1½% table n 19 quarters or 4¾ yearsNote: This leaves some money in the account but not enough for a full 6,000 withdrawal.3-36If 3,000 is deposited into an account paying 13.5% interest how much can be withdrawn eachyear indefinitely?Solution(A/P, i, ) iA (P)(i)A 3,000 .135 4053-37A grandfather gave his grandchild 100 for his 10th birthday. The child’s parents talked him intoputting this gift into a bank account so that when he had grandchildren of his own he could givethem similar gifts. The child lets this account grow for 50 years, and it has 100,000. What wasthe interest rate of the account?a.b.c.d.14.0%14.8%15.8%15.0%Solution 100,000 100(1 i)50

Chapter 3 Equivalence – A Factor Approach61i 14.8%The answer is c.3-38The annual cost to maintain a cemetery plot is 75. If interest is 6% how much must be set asideto pay for perpetual maintenance?a.b.c.d. 1,150 1,200 1,250 1,300SolutionP 75(P/A, 6%, ) 75(1/.06) 1,250The answer is c.3-39Henry Fuller purchases a used automobile for 6,500. He wishes to limit his monthly payment to 200 for a period of two years. What down payment must he make to complete the purchase if theinterest rate is 9% on the loan?SolutionP P' A(P/A, ¾%, 24)6,500 P' 200(21.889)P' 6,500 – 4,377.80 2,122.20 down payment3-40To start business, ECON ENGINEERING has just borrowed 500,000 at 6%, compoundedquarterly, which will be repaid by quarterly payments of 50,000 each, with the first payment duein one year. How many quarters after the money is borrowed is the loan fully paid off?Solutioni 6/4 1½%500,000 50,000(P/A, 1½%, n)(P/F, 1½%, 3)(P/A, 1½%, n) 500,000/[50,000(.9563)] 10.46From the 1½% table n 12 payments plus 3 quarters without payments equal 15 quartersbefore loan is fully paid off.

62Chapter 3 Equivalence – A Factor Approach3-41A bank is offering a loan of 20,000 with an interest rate of 12%, payable with monthly paymentsover a four year period.a.b.Calculate the monthly payment required to repay the loan.This bank also charges a loan fee of 4% of the amount of the loan, payable at the time of theclosing of the loan (that is, at the time they give the money to the borrower). What is theeffective interest rate they are charging?Solutiona.The monthly payments:i 12/12 1%,n (12)(4) 4820,000(A/P, 1%, 48) 526.00b.Actual money received P 20,000 - 0.04(20,000) 19,200A 526.00 based on 20,000Recalling that A P(A/P, i, n)526 19,200(A/P, i, 48)(A/P, i, 48) 526/19,200 0.02739for i 1¼% the A/P factor @ n 48 0.0278for i 1%the A/P factor @ n 48 0.0263by interpolation i 1 ¼[(.0263 - .02739)/(.0263 - .0278)]i 1.1817%Therefore ieff (1 0.011817)12 - 1 0.1514 15.14%3-42Find the present equivalent of the following cash flow diagram if i 18%.1000801602403204562074086098010100

Chapter 3 Equivalence – A Factor Approach63SolutionP 100 80(P/A, 18%, 10) - 20(P/G, 18%, 10) 172.483-43The annual worth of a quarterly lease payment of 500 at 8% interest is nearest toa.b.c.d. 2,061 2,102 2,123 2,253SolutionLease payments are beginning-of-period cash flows.First find the present worth of the quarterly payments at 8/4 2%.P 500 500(P/A, 2%, 3) 1,941.95A 1,941.95(1 .02)4 2,102The answer is b.3-44A 30-year mortgage of 100,000 at a 6% interest rate had the first payment made on September 1,1999. What amount of interest was paid for the 12 monthly payments of 2002?SolutionMonthly payment A 100,000(A/P, ½%, 360) 599.55Interest periods remaining Jan 1, 2002 331Jan 1, 2003 319P' 599.55(P/A, ½%, 331) 599.55(161.624) 96,901.67P'' 599.55(P/A, ½%, 319) 599.55(159.257) 95,482.53Interest 599.55(12) - (96,901.67 – 95,482.53) 5,775.463-45Holloman Hops has budgeted 300,000 per year to pay for labor over the next five years. If thecompany expects the cost of labor to increase by 10,000 each year, what is the expected cost ofthe labor in the first year, if the interest rate is 10%?SolutionA′ 300,000A′ A 10,000(A/G, 10%, 5)

64Chapter 3 Equivalence – A Factor Approach300,000 A 10,000(1.81)A 281,900 first year labor cost3-46For the cash flow shown below, determine the value of G that will make the future worth at theend of year 6 equal to 8,000 at an interest rate of 12% per year.YearCash Flow0016002600 G3600 2G4600 3G5600 4G6600 5GSolutionP 8,000(P/F, 12%, 6) 8,000(.5066) 4,052.804,052.80 600(P/A, 12%, 6) G(P/G, 12%, 6)4,052.80 600(4.111) G(8.930)G 177.633-47Big John Sipes, owner of Sipe’s Sipping Shine, has decided to replace the distillation machine hiscompany now uses. After some research, he finds an acceptable distiller that cost 62,500. Thecurrent machine has approximately 1200 lbs of copper tubing that can be salvaged and sold for 4.75/lb to use as a down payment on the new machine. The remaining components of thedistillation machine can be sold as scrap for 3,000. This will also be used to pay for thereplacement equipment. The remaining money will be obtained through a 10-year mortgage withquarterly payments at an interest rate of 8%. Determine the quarterly payment required to pay offthe mortgage. Also determine the effective interest rate on the loan.Solutioni 8/4 2%n (4)(10) 40P 62,500 - (1,200 x 4.75) - 3,000 53,800A 53,800(A/P, 2%, 40) 53,800(.0366) 1,969ieff (1 .02)4 - 1 8.24%3-48Ray Witmer, an engineering professor at UTM, is preparing to retire to his farm and care for hiscats and dogs. During his many years at UTM he invested well and has a balance of 1,098,000 inhis retirement fund. How long will he be able to withdraw 100,000 per year beginning today ifhis account earns interest at a rate of 4% per year?Solution

Chapter 3 Equivalence – A Factor ApproachA 100,000P 1,098,000 - 100,000* 998,00065*First withdrawal is today100,000 998,000(A/P, 4%, n)(A/P, 4%, n) 100,000/998,000(A/P, 4%, n) .1002Searching i 4% table, n 13 additional years of withdrawals, 14 total years of withdrawals3-49Abby W. deposits 75 per month into an account paying 9% interest for two years to be used topurchase a car. The car she selects costs more than the amount in the account. She agrees to pay 125 per month for two more years at 12% interest, and also uses a gift from her uncle of 375 aspart of the down payment. What is the cost of the car to the nearest dollar?Solutioni 9/12 ¾%n (12)(2) 24F 75(F/A, ¾%, 24) 75(26.189) 1,964.18 Amount in accounti 12/12 1%n (12)(2) 24P 125(P/A, 1%, 24) 125(21.243) 2,655.38 Amount repaid by loanTotal 1,964.18 2,655.38 375 4,994.56 4,995 Cost of automobile3-50The amount required to establish an endowment to provide an annual scholarship of 20,000requires a deposit into an account paying 8% is nearest toa.b.c.d. 1,600 25,000 250,000 500,000SolutionP 20,000(P/A, 8%, )P 20,000(1/.08)P 250,000The answer is c.3-51

66Chapter 3 Equivalence – A Factor ApproachAbby Motors offers to sell customers used automobiles with 400 down and payments for 3 yearsof 215 per month. If the interest rate charged to its customers is 12%, the cost of the automobileis nearest toa.b.c.d. 1,760 2,160 6,475 6,875Solutioni 12/12 1%n (12)(3) 36P 400 215(P/A, 1%, 36) 6,873.01The answer is d.3-52A tractor is bought for 125,000. What is the required payment per year to completely pay off thetractor in 20 years, assuming an interest rate of 6%?a.b.c.d. 1,150 5,550 10,900 12,750SolutionA 125,000(A/P, 6%, 20) 10,900The answer is c.3-53Jason W. bought a Mercedes when he came to UTM as an engineering student. The Mercedeswas purchased by taking a loan that was to be paid off in 20 equal, quarterly payments. Theinterest rate on the loan was 12%. Four years later, after Jason made his 16th payment, he gotmarried (no more dating!) and sold the Mercedes to his buddy Houston S. Houston madearrangements with Jason's bank to refinance the loan and to pay Jason's unpaid balance by making16 equal, quarterly payments at the same interest rate that Jason was paying. Three and ¼ yearslater, after Houston made his 13th payment, he flunked out of UTM (too many dates!) and sold thecar to Jeff M. Jeff paid the bank 2,000 cash (he had a good summer job!) to pay the loan balance.What was the amount of Jason's loan to purchase the Mercedes when it was new?Solutioni 12/4 3%

Chapter 3 Equivalence – A Factor Approach67Jason W.A P(A/P, 3%, 20)A P(.0672)Quarterly payment for JasonJason owesP .0672P(P/A, 3%, 4) .0672P(3.717) .2498PPresent worth of four remaining paymentsHouston S.A .2498P(A/P, 3%, 16) .2498P(.0796) .0199PQuarterly payment for HoustonJeff M.P .0199P(P/A, 3%, 3) .0199P(2.829) .0563PPresent worth of three remaining paymentsSet final payment equal to present worth of remaining payments2000 .0562PP 35,556.753-54A mortgage of 50,000 for 30 years, with monthly payments at 6% interest is contemplated. Atthe last moment you receive news of a 25,000 gift from you parents to be applied to the principal.Leaving the monthly payments the same, what amount of time will now be required to pay off themortgage and what is the amount of the last payment (assume any residual partial payment amountis added to the last payment)?Solutioni 6/12 ½%n (12)(30) 360 periodsA 50,000(A/P, ½%, 360) 299.77 monthly payment(Note: For more accurate answerAfter reduction of P to 25,00025,000 299.77(P/A, ½%, n)(P/A, ½%, n) 83.40Try n 104 periods: P/A 80.942Try n 120 periods: P/A 90.074Interpolate, n 108.31 periods 9.03 yearsAt 9 years (108 periods): P 299.77(P/A, ½%, 108) 299.77(83.2934)factor was used)

68Chapter 3 Equivalence – A Factor Approach 24,968.87Residual 25,000 - 24,968.87 31.13Last Payment Value of residual at time of last payment last payment 31.13(F/P, ½%, 108) 299.77 353.123-55A person would like to retire 10 years from now. He currently has 32,000 in savings, and heplans to deposit 300 per month, starting next month, in a special retirement plan. The 32,000 isearning 8% interest, while the monthly deposits will pay him 6% nominal annual interest. Oncehe retires, he will deposit the total of the two sums of money into an account that he expects willearn a 4% annual interest rate. Assuming he will only spend the interest he earns, how much willhe collect in annual interest, starting in year 11?SolutionSavings:F 32,000(F/P, 8%, 10) 69,086Monthly deposits:i 6/12 ½%n (12)(10) 120F 300(F/A, ½%, 120) 49,164The total amount on deposit at the end of year 10 isFT 69,086 49,164 118,250The interest to collect per year 118,250 0.04 4,7303-56Using the tables for uniform gradients, solve for the future value at the end of year 7 if i 10%. 500 400 300 200 10001234 100 100SolutionPV 100(P/G, 10%, 7) - 100(P/A, 10%, 7) - 100 689.50FV 689.5(F/P, 10%, 7) 1,343.84567

Chapter 3 Equivalence – A Factor Approach 51 b. 1,191 c. 1,197 d. 2,898 Solution i 6/12 ½% n (12)(3) 36 F P(1