Assume that you purchase a 4-year savings certificate for 1000 with an 10% annual interest. "1. Assume semi-annual compouding, what is the value of the certifacate when it matures?" "2. Assume annual compouding, what is the value of the certifacate when it matures?" 0 1 2 3 4 0 1 2 3 4 5 6 7 8 1000.0 1100.0 1210.0 1331.0 1464.1 SpreadSheet Approach 1000.0 1050.0 1102.5 1157.6 1215.5 1276.3 1340.1 1407.1 1477.5 SpreadSheet Approach 1464.1 Formula Approach 1477.5 Formula Approach PV 1000 IR 0.1 n 4 ##### Sheet/List 2 ##### You are asked to lend 200 in return for 300. "1. If you receive 300 in 4 years, what annual interest rate has been offered to you?" 0 1 2 3 4 200.0 221.3 244.9 271.1 300.0 PV 200 FV 300 n 4 IR 10.67% SpreadSheet Approach IR 10.67% Formula Approach ##### Sheet/List 3 ##### "In January 2013, the core inflation rate in Venezuela was about 23%. How long it takes (in months) for purchasing power to be cut in half? In September 2018 the inflation rate in Venezuela was about 480000%. How long it takes (in days) for purchasing power to be cut in half?" PV 0.5 FV 1 inflation 0.23 years 3.35 months 40.20 PV 0.5 FV 1 inflation 4800 years 0.08 days 29.2 ##### Sheet/List 4 ##### You are offered 2000 for an investment that gives you 500 at the end of the next 4 years. Returns on similarly risky assets are currently at the 4%. If the returns on similarly risky assets would increase to 7% is it true that the value of this investment also increases? 0 1 2 3 4 4 500 500 500 500 interest rate 0.07 467.3 436.7 408.1 381.4 PV 1693.61 Spreadsheet approach PV 1693.61 Formula approach ##### Sheet/List 5 ##### "You have applied for a mortgage of 240000 to finance the purchase of a new home. The bank will require you to make annual payments of 9600 at the end of each 30 years. Determine the interest rate in effect on this mortgage. If this is an amortized loan, how much principal will be repaid in the first and the last year?" Loan balance Interest Principal PMT 9600 0 PV 240000 1 9600 9484.38 240000 2926 6674 Spreadsheet approach FV 288000 0.6% 2 9600 9370.15 233326 2844 6756 Interest 1.219% 3 9600 9257.29 226570 2762 6838 years 30 4 9600 9145.80 219732 2679 6921 0.01 5 9600 9035.65 212811 2594 7006 6 9600 8926.82 205805 2509 7091 7 9600 8819.31 198714 2422 7178 8 9600 8713.09 191537 2335 7265 9 9600 8608.15 184272 2246 7354 10 9600 8504.47 176918 2157 7443 11 9600 8402.04 169475 2066 7534 12 9600 8300.85 161941 1974 7626 13 9600 8200.87 154315 1881 7719 14 9600 8102.10 146596 1787 7813 15 9600 8004.52 138784 1692 7908 16 9600 7908.11 130875 1595 8005 17 9600 7812.87 122871 1498 8102 18 9600 7718.77 114769 1399 8201 19 9600 7625.81 106568 1299 8301 20 9600 7533.96 98267 1198 8402 21 9600 7443.22 89865 1096 8504 22 9600 7353.58 81361 992 8608 23 9600 7265.01 72752 887 8713 24 9600 7177.51 64039 781 8819 25 9600 7091.06 55220 673 8927 26 9600 7005.66 46293 564 9036 27 9600 6921.28 37258 454 9146 28 9600 6837.92 28112 343 9257 29 9600 6755.57 18855 230 9370 30 9600 6674.20 9484 116 9484 ##### Sheet/List 6 ##### "You are a manager and want to allow your customers to buy on credit with 3 months until they pay your accounts payable. Meanwhile you need to finance those accounts payable and you resort to a bank credit given to you at the 6% annually with monthly compounding. What (minimum) interest rate (in annual terms) should you give your costumer so, that you cover you costs from the short-term bank credit?" Bank Customer Nominal annual 0.06 Nominal annual 6.03% Monthly compounding 12 Compounding 3 EAR (EFF) 6.17% EAR (EFF) 6.17% ##### Sheet/List 7 ##### Assume that you purchase a 6-year savings certi cate for 1000 with an 8% interest compounded annually. Calculate the value of the certificate when it matures (future value). 0 1 2 3 4 5 6 1000.0 1080.0 1166.4 1259.7 1360.5 1469.3 1586.9 SpreadSheet Approach 0.08 1586.9 Formula Approach ##### Sheet/List 8 ##### "Assume that you purchase a 6-year savings certi cate for 1000 with an 8% annual interest compounded semiannually. Calculate the value of the certi cate when it matures (future value)." 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 0 1 2 3 4 5 6 7 8 9 10 11 12 1000.0 1040.0 1081.6 1124.9 1169.9 1216.7 1265.3 1315.9 1368.6 1423.3 1480.2 1539.5 1601.0 SpreadSheet Approach 0.08 1601.0 Formula Approach ##### Sheet/List 9 ##### You are asked to lend 500 in return for 600 after two years. What annual interest rate has been offered to you? Formula approach Spreadsheet approach 0 1 2 0 1 2 PV 500 547.7225575 600 PV 500 547.7227213 600.0003589 i 9.54% i 9.54% FV 600 FV 600 ##### Sheet/List 10 ##### In the past 10 years the inflation rate in Turkey was about 8%. How long it takes (to the nearest year) for the purchasing power to be cut in half? How would the result change with a much lower 4% inflation rate? Check PV 0.5 year 1 2 3 4 5 6 7 8 9 FV 1 FV 0.54 0.58 0.63 0.68 0.73 0.79 0.86 0.93 1.00 inflation 0.08 PV 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 years 9.01 inflation 0.04 years 17.67 ##### Sheet/List 11 ##### How much would you be willing to pay today for an investment that would return 800 at the end of each year for the next 6 years? Assume a discount rate of 5%. 0 1 2 3 4 5 6 6 800 800 800 800 800 800 interest rate 0.05 761.9 725.6 691.1 658.2 626.8 597.0 PV 4060.55 Spreadsheet approach PV 4060.55 Formula approach ##### Sheet/List 12 ##### "You have applied for a mortgage of 140000 to finance the purchase of a new home. The bank will require you to make annual payments of 6600 at the end of each 30 years. Determine the interest rate in effect on this mortgage. If this is an amortized loan, how much principal will be repaid in the second year?" Loan balance Interest Principal PV 140000 Loan balance Interest Principal PV 60000 0 FV 198000 1.16% 0 FV 140951 1 6600 6445.31 140000 3360 3240 Spreadsheet approach Interest 2.4% 1 7047.55 6406.87 60000.0 6000.0 1047.6 Spreadsheet approach Interest 10.0% 2 6600 6294.25 136760 3282 3318 years 30 2 7047.55 5824.43 58952.4 5895.2 1152.3 years 20 3 6600 6146.73 133442 3203 3397 3 7047.55 5294.93 57800.1 5780.0 1267.6 4 6600 6002.67 130045 3121 3479 "Now, to understand what is going on, imagine that you pay-off the mortage in one instalment at the end of the period, i.e. 6600 x 30 = 198000. What is the annual interest rate? It is (198000/140000)^(1/30) = 1.16% not much. I would like to have a mortgage like that. However, we are paying at the end of each year. So compared to the previous situation you loose the opportunity to invest 6600 because you pay that money to the bank! Or equivalently, the bank has the ability to re-invest those 6600 they receive from you. Remember, financial management is a lot about alternatives and opportunity costs. Now, we have to find this re-investment rate and we are going to find it using a discounting approach." 4 7047.55 4813.58 56532.5 5653.2 1394.3 5 6600 5861.98 126566 3038 3562 5 7047.55 4375.98 55138.2 5513.8 1533.8 6 6600 5724.59 123004 2952 3648 6 7047.55 3978.17 53604.5 5360.4 1687.1 7 6600 5590.42 119356 2865 3735 7 7047.55 3616.52 51917.3 5191.7 1855.8 8 6600 5459.39 115620 2775 3825 8 7047.55 3287.74 50061.5 5006.1 2041.4 9 6600 5331.44 111795 2683 3917 9 7047.55 2988.86 48020.1 4802.0 2245.6 10 6600 5206.48 107878 2589 4011 10 7047.55 2717.15 45774.5 4577.4 2470.1 11 6600 5084.46 103867 2493 4107 11 7047.55 2470.13 43304.4 4330.4 2717.1 12 6600 4965.29 99760 2394 4206 12 7047.55 2245.58 40587.3 4058.7 2988.8 13 6600 4848.91 95554 2293 4307 13 7047.55 2041.43 37598.4 3759.8 3287.7 14 6600 4735.27 91248 2190 4410 14 7047.55 1855.85 34310.7 3431.1 3616.5 15 6600 4624.29 86837 2084 4516 15 7047.55 1687.14 30694.2 3069.4 3978.1 16 6600 4515.90 82322 1976 4624 16 7047.55 1533.76 26716.1 2671.6 4376.0 17 6600 4410.06 77697 1865 4735 17 7047.55 1394.33 22340.1 2234.0 4813.5 18 6600 4306.70 72962 1751 4849 18 7047.55 1267.57 17526.6 1752.6 5294.9 19 6600 4205.76 68113 1635 4965 19 7047.55 1152.34 12231.6 1223.2 5824.4 20 6600 4107.19 63148 1516 5084 20 7047.55 1047.58 6407.3 640.7 6406.8 21 6600 4010.93 58063 1394 5206 59999.94 22 6600 3916.92 52857 1269 5331 23 6600 3825.12 47525 1141 5459 24 6600 3735.47 42066 1010 5590 25 6600 3647.92 36476 875 5725 26 6600 3562.42 30751 738 5862 27 6600 3478.93 24889 597 6003 28 6600 3397.39 18886 453 6147 29 6600 3317.76 12740 306 6294 30 6600 3240.00 6445 155 6445 139999.95 0 ##### Sheet/List 13 ##### A company is offereing bonds which pay 100 per year indefinitely. If you require a 12% return on these bonds (the discount rate) what is the value of each bond today? Formula approach Spreadsheet approach 833.332299 PMT 100 1 89.28571429 Interest rate 0.12 2 79.71938776 PV 833.33 3 71.17802478 4 63.55180784 5 56.74268557 6 50.66311212 7 45.23492153 8 40.3883228 9 36.0610025 10 32.19732366 11 28.74761041 12 25.66750929 13 22.91741901 14 20.46198126 15 18.26962613 16 16.31216618 17 14.56443409 18 13.00395901 19 11.61067769 20 10.36667651 21 9.255961168 22 8.264251043 23 7.378795574 24 6.588210334 25 5.882330655 26 5.252080942 27 4.689357984 28 4.186926771 29 3.738327475 30 3.337792388 31 2.980171775 32 2.660867656 33 2.375774693 34 2.121227405 35 1.89395304 36 1.6910295 37 1.509847768 38 1.348078364 39 1.203641396 40 1.074679818 41 0.959535552 42 0.856728171 43 0.764935867 44 0.682978453 45 0.60980219 46 0.544466241 47 0.486130573 48 0.434045154 49 0.387540316 50 0.346018139 51 0.308944767 52 0.275843542 53 0.246288877 54 0.219900783 55 0.196339985 56 0.175303558 57 0.156521034 58 0.139750923 59 0.12477761 60 0.11140858 61 0.099471947 62 0.088814238 63 0.079298427 64 0.070802167 65 0.06321622 66 0.056443054 67 0.050395584 68 0.044996057 69 0.040175051 70 0.035870581 71 0.032027305 72 0.028595808 73 0.025531971 74 0.022796403 75 0.020353931 76 0.018173153 77 0.016226029 78 0.014487526 79 0.012935291 80 0.011549367 81 0.010311935 82 0.009207085 83 0.008220611 84 0.007339832 85 0.006553421 86 0.005851269 87 0.005224347 88 0.004664596 89 0.004164818 90 0.003718587 91 0.003320167 92 0.002964435 93 0.002646817 94 0.002363229 95 0.002110026 96 0.001883952 97 0.0016821 98 0.001501875 99 0.00134096 100 0.001197286 101 0.001069005 102 0.000954469 103 0.000852204 104 0.000760897 105 0.000679372 106 0.000606582 107 0.000541591 108 0.000483564 109 0.000431753 110 0.000385494 111 0.000344191 112 0.000307313 113 0.000274387 114 0.000244988 115 0.00021874 116 0.000195303 117 0.000174378 118 0.000155695 119 0.000139013 120 0.000124119