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 2 ##### 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 3 ##### "You are offered an investment opportunity with the 'guarantee' that your investment will double in 5 years. Assuming annual compounding, what annual rate of return would this investment provide?" 0 1 2 3 4 5 PV 1000 1148.698293 1319.507768 1515.716321 1741.10075 1999.99946 Spreadsheet approach interest 14.87% 14.87% Formula approach FV 2000 ##### Sheet/List 4 ##### "You just bought a new Play Station. However, you expect that in five years a new version will be put on the market, so you start saving now. If you put 100 at the end of each year for the next 5 years into your saving account that pays 3% annually, how much will you accumulate after 5 years with compounding? How much will you accumulate if you put 100 at the beginning of each year?" 0 1 2 3 4 5 0 1 2 3 4 5 PMT 100 100.00 103.00 106.09 109.27 112.55 100 115.93 112.55 109.27 106.09 103.00 interest 0.03 100.00 103.00 106.09 109.27 100.00 115.93 112.55 109.27 106.09 years 5 100.00 103.00 106.09 100.00 115.93 112.55 109.27 100.00 103.00 100.00 115.93 112.55 100.00 100.00 115.93 Spreadsheet approach 1 530.91 FV Spreadsheet approach 1 546.84 FV 0 1 2 3 4 5 FV 0 1 2 3 4 5 FV 112.55 109.27 106.09 103.00 100.00 530.91 115.9274074 112.550881 109.2727 106.09 103 546.84 Spreadsheet approach 2 Spreadsheet approach 2 Formula approach 530.9 Formula approach 546.8 ##### Sheet/List 5 ##### 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 6 ##### "You are a manager and want to allow your customers to buy on credit with 4 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 18% annually with monthly compounding. What 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 0.18 Nominal annual 18.41% Compounding 12 Compounding 3 EAR (EFF) 19.56% EAR (EFF) 19.56% ##### Sheet/List 7 ##### "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