Do the Math 9 4 Refinancing a Mortgage Kevin Tutumbo of Terre Haute, Indiana, has owned his home for 15 years and expects to live in it for at least five more He originally borrowed $135,000 at 6 5 percent interest for 30 years to buy the home He still owes $96,000 on the loan Interest rates have since fallen to 5 5 percent, and Kevin is considering refinancing the loan for 15 years He would have to pay 2 points on the new loan with no prepayment penalty on the current loan a What is Kevin's current monthly payment Round Estimating Mortgage Loan Payments for Principal and Interest in your intermediate calculations to four decimal places Use Table 9 4 Round your answer to the nearest cent b Calculate the monthly payment on the new loan (Note The points on the new mortgage are not included in the mortgage amount ) Round Estimating Mortgage Loan Payments for Principal and Interest in your intermediate calculations to four decimal places Use Table 9 4 Round your answer to the nearest cent C Advise Kevin on whether he should refinance his mortgage usino the Run the Numbers worksheet, When You Should Refinance Your Mortgage Round Future value of a series of Equal Amounts and Future value of a Single Amount in your intermediate calculations to four decimal places Use Appendix A 1 and Appendix A 3 Assume the annual savings, prepayment penalty, and closing costs can be invested at 3 percent after taxes Kevin refinance his mortgage Select should shouldn't Future Value of a Series of Equal Amounts (an Annuity of $1 Paid at the End of Each Period) (Used to Compute the Compounded Future Value of a Stream of Income Payments) 3 5 49211 n 1 2 4 6 8 9 10 11 12 13 14 15 16 17 18 19 20 1 1 0000 10000 10000 1 0000 1 0000 10000 1 0000 1 0000 1 000 1 0000 1 0000 10000 1 0000 1 0000 1 000 1 0000 10000 10000 1 0000 1 0000 2 20100 20200 20300 20400 2 0500 2 000 2 0700 20800 2 0900 21000 21100 2 1 200 2 1300 2 1400 21500 2 1600 21700 21800 2 1900 27000 3 3 0301 3 0604 3 0909 3 1216 3 1525 3 1836 3 2149 3 2464 3 2781 33100 3 3421 33744 3 4069 3 696 34725 3 5056 35389 3 5724 3 6051 3 6400 40604 41216 4 1836 42465 43101 43746 44399 49061 45731 46410 47097 47793 48198 4994 5 105 52154 5 2013 5 5 1010 5 2040 53091 54163 55756 5 6371 5 7907 58606 59847 6 1051 6 2278 63528 6403 6 6101 67424 68771 720144 7 1542 72966 7 4416 6 6 1520 63051 66330 68019 6 9753 71533 73399 7 5233 7 7156 7 9129 8 1152 83227 8 555 8 7537 8 9775 9 2018 94420 9 6830 9 99 7 72135 74143 76625 789838 1420 8 3938 8 6540 8 9278 9 2004 94872 9 7833 10 0890 104047 10 7305 11 0668 11 4139 11 7720 12 1415 12 5227 12 9159 82857 85830 8 8923 92142 95491 9 8975 10 2598 10 6366 110285 11 4359 11 8594 12 2997 12 7573 13 2328 13 7268 14 2401 14 7733 153270 15 9020 16 4991 9 93685 9 7546 10 1591 105828 11 0266 11 4913 11 9780 12 4876 13 0210 13 5795 14 1640 147757 15 4157 16 0853 16 7858 17 5185 18 2847 19 0859 19 9234 20 78 10 10 4622 10 9497 11 4639 12 0061 12 5779 13 1808 13 8164 14 4866 15 1929 15 9374 167220 17 5487 18 4197 19 3373 20 3637 213215 22 3931 23 5213 247089 259927 11 11 5668 12 1687 12 8078 13 464 14 2068 149716 15 7836 16 6455 17 5603 18 5312 19414 205546 218143 23 0445 243493 25 7329 27 1999 28 7551 30 4035 22 1504 12126825 13 4121 14 1920 15 0258 159171168699 17 8885 18 977120 1407 21 3843 22 7132 241331 25 5502 27 2707 29 0017 30 8502 32 8229 349311 37 1802 39 5805 13 13 8093 14 6803 1 56178 166268 177130 18 8821 201406 21 4953 22 9534 24 5227 26 2116 28 0291 29 9847 32 0887 343519 36 7862 39 4000 47 2187 45 2445 14 14 9474 159739 17 0863 18 2919 19 5986 21 0151 22 5505 24 2149 26 0192 27 9750 30 0949 32 3926 348827 37 5811 40 5047 43 6720 47 1027 508180 54 8409 59 1959 15 16 0969172934 18 5989 200236 215786 23 2760 25 1290 27 1521 29 3609 31 7725 34 4054 37 2797 40 4175 3 8424 47 5804 51 6595 56 1101 60 9653 66 2607 720351 16 17 2579 186393 20 1569218245 25575 256725278881 30 3243 33 0034 35 9497 39 1899 42 7533 166717 50 9804 55 7175 60 9250 66 5488 72 9390 18502 17 18 4304 200121 21 7616 2369755 8404 282129308402 33 7502 5 9737 40547 TOOR 88837 53 7391 59 1176 65 0751 71 6730 789791 370680 960217 1059306 18 19 6147 214123 23 4144256454 28 1324 309057 33 9990 37 450241 3013 45 5992 50 3959 55 7497 61 7251 68 3961 75 8364 841402 93 4056 103 7403 115 2659 128 1167 19 208109228406 25 1169 276712 30 539033 7600 37 3790 41 4463 460185 511591 56 939 634397 70 7494 789692 88 2118 986032 110 2846 1234135 138 1664 154 7400 20 22 0190 24 2974 268704 297781 330660 36 7856 409955 45 7620511601 57 2750 642078720524 809468 910249102 4436 1153797 30 0329166280 165 4180 186 6880 21 23 2392 25 7833 286765 319692 35 7193 39 9927 448652 50 422956 7645 540025 72 2651 816987 92 46991047684 118 8101 134 8405 152 1385170210 197 81742750256 22 24 4716 27 2990 30 5368 342680 3850524392349 0057 55 4568 628733 714027 81 21 92 5006 105 610 120 4360 1376316 157 4150 1801721206 348 236 4384 271 0307 23 257163 288450 32 4529356179 414305 66 958 53 4361 60 8933695319 725830 91 16 1046019 120 2018 138910 1592764 53 6014 211 301324448682023518 326 2368 24 269735304219 344265 390826 445020 50 8156 58 1767 380973702 1741 18 1552 1368315 1586556 1341678 213 976 28 8075 2894945 3370105 3926542 25 28242320303 36 4593 416459 47 7271 518645 63 2490 73 1059347003 983471 1144133 133 33391556196 181 8708 212 7930 249 21402 92 101 42 6035 4020424 471 9811 26 29 5256 336709 111 38 5530 43117 68 6765 51 1135 79 9544 9111100118 58 1564 1503339 176 8501 208 3327 245 7120 567 3773 2900883 312 7626 4052721 4794305 308209 35343 40 7096 70M2 546691 61 705374 418 87 350 272 11 1 0 10 2003406 238 1993 283 5638 337 5024 681 8527 40203234792211 571 5223 32 1291 429309 370512 39676 584026 685281 5 38 1126 1 0 4723718 17 327 1041 392 5027 566 4808 681 1116 819 7233 33 45048722 452188 59063 3227 7368 7365103 565914151 61) 11 585311 312 313721697 4563032 552 5120 669 4474 8115228 8 113 837 136 135 34784940568175754 5609 643890587 1 1 9678341451 530 311 647 4350 7909479 9567121 115132 57313176701 10488864604020 754013502551079815476701926351398056537 101101005 1773090 5529 829 2350 75731345224163212 7343 856 10 11279691526671 30334807503359406 5289737701 8150816VOR M 50614632845794 IN S A 7 212 714 10056515089 50 21813 09 3151533 45497 17 Future Value of a Single Amount ($1 at the End of n Periods) (Used to compute the Compounded Future Value of a Known Lump Sum) 8 9 10 129 134 7 10700 1 000 1 0900 1 100 1 1100 1 1200 1 1300 1 1449 1 1664 1 1881 1 2100 n 1 2 3 4 5 1221 1 2544 1 2769 1 2597 1 2950 14049 14429 1 2250 13108 14026 13605 1 4116 1 5181 1 5735 16305 14683 1 5396 1 9254 1 5869 16771 18704 2 0820 1 5007 16058 1 9738 2 2107 1 7138 18280 2 0762 2 3526 17182 1 8909 19926 24760 2 6584 9 18385 1990 21719 23674 2 5931 2 7731 3 1058 3 4785 38960 3 0040 3 3946 3 8359 28531 2 5804 28127 3 1384 43345 11 12 13 14 15 1 9672 2 1589 2 1049 23316 2 2522 2 5182 2 4098 27196 2 5785 29372 2 75903 1722 229522 34259 3 4523 43535 4 8980 3 0658 33417 1 2 3 4 5 6 1 0100 10200 1 0300 1 000 1 0500 10600 1 0201 10404 1 0609 1 0816 1 1025 1 1236 1 0303 1 0612 1 0927 1 1249 1 1576 1 1910 1 0406 10824 1 1255 1 1699 1 2155 12625 10510 1 1041 1 1993 1 2167 1 276 13382 1 0615 1 1262 1 1941 1 2653 1 3401 14185 10721 1 1487 1 2299 13159 1 4071 1 5036 1 0829 1 1717 1 2668 1 3686 1 4775 1 5938 10937 1 1951 13048 1 4233 1 5513 16995 1 1046 1 2190 13439 1 4802 1 6289 1 7908 1 1157 1 2434 13842 1 5395 1 7103 18983 1 1268 1 2682 14258 16010 1 1959 20122 1 1381 12936 14685 16651 1 8856 2 1329 1 1495 1 3195 15126 1 73171 9799 2 2609 1 1610 1 3459 15580 1 8009 2 0789 23966 1 1726 1 3728 16047 1 87302 1829 2 5404 1 1843 1 4002 16528 1 9479 2 2920 26928 1 1961 1 4282 1 7024 2 0258 2 4066 28543 1 2081 14568 1 7535 2 1068 2 5270 30256 1 2202 14859 18061 2 1911 2 65333 2071 1 2324 15157 18603 2 2788 27860 33996 1 9161 2 3699 2 9253 36035 1 2572 15769 19736 2 464730715 38197 2 0328 2 5633 3 2251 40689 16406 2 0938 2 6658 3 386642919 2 1566 2 7725 3 5557 45494 1308217069 2221388343 733548223 13213 1 7410 22879 29987 3 9201 5 1117 1 7758 23566 3 1187 4 1161 54184 B114 24273 3 2434 4321957435 22080 32620 48010 70100 102857 15446 2 6916 4389 71057 11 4674 184202 3 6425 3 7975 4 1772 4 5950 4 8871 5 4736 6,1304 5 5348 6 2543 7 0673 14 15 16 17 18 19 20 1 1400 1 1500 1 1600 1 1700 1 1800 1 1900 2000 1 2996 13225 1 3456 13689 1 39 24 1 4161 1 4400 1 4815 15209 1 5609 1 6016 1 6430 1 6852 1 7280 1 6890 1 7490 18106 18739 1 9388 2 0093 20736 2 0114 2 1003 2 1924 2 7878 23864 26883 2 1950 2 3131 2 4364 2 5652 2 6996 2 8398 2 9860 25023 2 6600 2 8262 30012 3 1855 33793 35832 2 8526 3 0590 3 7784 3 5115 3 7509 40214 42998 3 2519 3 5179 2030 4 1084 4 7854 5 1598 3 7072 4 0456 4,4114 48068 5 2338 5 6947 6 1917 4 2262 4 6524 5 1173 56240 6 1759 6 7767 7 801 4 8179 5 3503 5 9360 65801 72876 8 0542 9161 5 4934 6 1528 6 8858 76987 8 5994 9 5964 10 6993 6 2613 7 0757 7 9875 9 0075 10 1472 11 4198 12 8392 7 1379 8 1371 9 2655 10 5387 11 9737 13 5895 154070 8 1372 9 3576 107480 12 3303 141290 16 1715 18 6884 9 2765 10 7613 12 4677 14,4265 16 6722 19 2441 22 1861 10 5752 123755 14 4625 16 8790 19 6733 22 9005 26 6233 12 0557 14 2318 16 7765 197484 23 2144 27 2516 319480 13 7435 163665 19 4608 23 1056 27 3930 32 4294 383376 15 626 18 3215 22 5745 270336 323238 38 5910 46 0051 17 3510 21 6447 26 1864 316293 38 1421 45 9233 55 2061 20 36 16 24 8915 303762 3700624 5 0076 546487 66 2474 28 6252 35 2361 3 2973 53 1090 65 0320 79 4968 32 9190 40 8742 506578 62 6686 77 3881 95 3962 47 4141 59 2697 73 9490 92 0918 114 4755 13 5353 550004 593455 87 2598 109 5893373706 50 0656 63 2004 81 1342 102 9566 130 4112 164 8147 57 5755 740085 949271 121 5005 155 189 197 8136 1110647 1433706184 6753 2373763 67 5635 378 7212 5338587 75037831051668 1469772 2330 1030 657 1670 704256615 392735759889149100438 53101 39703 43276 17 3 1583 3 7000 58951 6 8660 50545 5 5599 3 3799 3 9960 4 7171 6 9436 7 6900 7 9861 9 0243 10 1974 361654 3157 5 1417 6 1159 72633 86128 96453 38697 56044 6 7225 11 5231 46610 50338 4 1405 6 1088 10 8038 130211 4430454365 6 6586 12 1003 14,7138 7905 5871572579 110253 13 5523 15 1285 86231 50724 6341 79111 54274 68085 58074 7 394 93992 6213979851 102051 65688 6271 111671 71143 9 3173 12 1722 76123100627 13 7677 149745 217245 314094 294570 46 9016 743575 1400 117 30 RUN THE NUMBERS When You Should Refinance Your Mortgage It is sometimes advantageous to refinance an existing mortgage when interest rates dedine In mortgage refinancing, a new mortgage is obtained to pay off and replace an existing mortgage Most often it is undertaken to lower the monthly payment on the home by taking out a new loan with a lower interest rate The example here illustrates how to determine whether refinancing your mortgage is a wise choice The original mortgage for $160,000 was obtained seven years ago at a 5 5 percent interest rate for 30 years The monthly pay ment is $908 After seven years, the principal owed has declined to $142,100 If interest rates for new mortgages have declined to 4 5 percent, the owner could take out a new mortgage at the lower rate for a monthly payment of $827 Borrowing $142,100 for 23 years at 4 5 percent saves approximately 581 per month (5908 $827) How ever, refinancing may have some up front costs, including a possible prepayment penalty on the old mort gage and closing costs for the new mortgage The question then becomes, will these costs exceed the monthly savings gained with a DO IT IN CLASS lower payment The following worksheet provides a means for estimat ing whether refinancing offers an advantage It compares the future value of the reduced monthly payments (line 5) with the future value of the money used to pay the up front costs (estimated here at 2 ) of refinancing (line 8) The homeowner would need to estimate the number of months he or she ex pects to own the home after refinancing Given an estimate of four years in this example, the net savings would be $977 (sub tracting line 8 from line 5), and refinancing would benefit the owner In this example, planning to live in the home only three more years would result in it not being financially advantageous to refinance A similar worksheet can be found at www bankrate com calculators mortgages refinance calculator aspx Your Figures Example $908 827 81 4,175 Decision Factors 1 Current monthly payment 2 New monthly payment 3 Monthly savings (line 1 line 2) 4 Additional years you expect to live in the house 5 Future value of an account balance after 4 years if the monthly savings were invested at 3 after taxes (using the calculator on the Garman Forgue companion website) 6 Prepayment penalty on current loan (0 ) 7 Points and fees for new loan (2 ) 8 Future value of an account balance after 4 years if the prepayment penalty and closing costs (54,263) had been invested instead at 3 after taxes (using the calculator on the Garman Forgue companion website) 9 Net saving after 48 months dine 5 line 8) 2,842 3,198 $977 It may also be possible to borrow more than the current balance owed on the existing loan, thereby utilizing some of the equity built up in the home Borrowers refinancing for more than the amount owed should understand that rebuilding the equity to its previous level may take many years This also is dangerous because if home prices decline the borrower will owe more on the home than it is worth Table 9 4 Estimating Mortgage Loan Payments for Principal and Interest (Monthly Payment per $1,000 Borrowed) 5 5 Payment Period (Years) Interest Rate ( ) 15 20 25 30 3 0 $6 9058 $5 5460 $4 7421 $4 2160 3 5 7 1488 5 7996 5 0062 4 4904 4 0 7 3969 6 0598 5 2783 4 7742 4 5 7 6499 6 3265 5 5583 5 0669 5 0 7 9079 6 5996 5 8459 5 3682 8 1708 6 8789 6 1409 5 6779 6 0 8 4386 7 1643 6 4430 5 9955 6 5 8 7111 7 4557 6 7521 6 3207 7 0 8 9883 7 7530 7 0678 6 6530 7 5 9 2701 8 0559 7 3899 6 9921 8 0 9 5565 8 3644 Note To use this table to figure a monthly mortgage payment, divide the amount borrowed by 1,000 and multiply by the 7 7182 7 3376 ppropriate figure in the table for the interest rate and time period of the loan For example, a 5160,000 loan for 30 years 60 percent would require a payment of $959,280 (5160,000 1,000) X 5 9955), over 20 years, it would require a ayment of $1,146 29 (5160,000 1,000) X 7 1643 For calculations for different interest rates, visit the Garman Forgue ompanion website

Question

Do the Math 9 4 Refinancing a Mortgage Kevin Tutumbo of Terre Haute, Indiana, has owned his home for 15 years and expects to live in it for at least five more  He originally borrowed $135,000 at 6 5 percent interest for 30 years to buy the home  He still owes $96,000 on the loan  Interest rates have since fallen to 5 5 percent, and Kevin is considering refinancing the loan for 15 years  He would have to pay 2 points on the new loan with no prepayment penalty on the current loan  a  What is Kevin's current monthly payment  Round Estimating Mortgage Loan Payments for Principal and Interest in your intermediate calculations to four decimal places  Use Table 9 4  Round your answer to the nearest cent  b  Calculate the monthly payment on the new loan  (Note  The points on the new mortgage are not included in the mortgage amount ) Round Estimating Mortgage Loan Payments for Principal and Interest in your intermediate calculations to four decimal places  Use Table 9 4  Round your answer to the nearest cent  C  Advise Kevin on whether he should refinance his mortgage usino the Run the Numbers worksheet,  When You Should Refinance Your Mortgage Round Future value of a series of Equal Amounts and Future value of a Single Amount in your intermediate calculations to four decimal places  Use Appendix A 1 and Appendix A 3  Assume the annual savings, prepayment penalty, and closing costs can be invested at 3 percent after taxes  Kevin refinance his mortgage  Select should shouldn't Future Value of a Series of Equal Amounts (an Annuity of $1 Paid at the End of Each Period) (Used to Compute the Compounded Future Value of a Stream of Income Payments) 3  5  49211 n 1  2  4  6  8  9  10  11  12  13  14  15  16  17  18  19  20  1 1 0000 10000 10000 1 0000 1 0000 10000 1 0000 1 0000 1 000 1 0000 1 0000 10000 1 0000 1 0000 1 000 1 0000 10000 10000 1 0000 1 0000 2 20100 20200 20300 20400 2 0500 2 000 2 0700 20800 2 0900 21000 21100 2 1 200 2 1300 2 1400 21500 2 1600 21700 21800 2 1900 27000 3 3 0301 3 0604 3 0909 3 1216 3 1525 3 1836 3 2149 3 2464 3 2781 33100 3 3421 33744 3 4069 3 696 34725 3 5056 35389 3 5724 3 6051 3 6400 40604 41216 4 1836 42465 43101 43746 44399 49061 45731 46410 47097 47793 48198 4994 5 105 52154 5 2013 5 5 1010 5 2040 53091 54163 55756 5 6371 5 7907 58606 59847 6 1051 6 2278 63528 6403 6 6101 67424 68771 720144 7 1542 72966 7 4416 6 6 1520 63051 66330 68019 6 9753 71533 73399 7 5233 7 7156 7 9129 8 1152 83227 8 555 8 7537 8 9775 9 2018 94420 9 6830 9 99 7 72135 74143 76625 789838 1420 8 3938 8 6540 8 9278 9 2004 94872 9 7833 10 0890 104047 10 7305 11 0668 11 4139 11 7720 12 1415 12 5227 12 9159 82857 85830 8 8923 92142 95491 9 8975 10 2598 10 6366 110285 11 4359 11 8594 12 2997 12 7573 13 2328 13 7268 14 2401 14 7733 153270 15 9020 16 4991 9 93685 9 7546 10 1591 105828 11 0266 11 4913 11 9780 12 4876 13 0210 13 5795 14  1640 147757 15 4157 16 0853 16 7858 17 5185 18 2847 19 0859 19 9234 20 78 10 10 4622 10 9497 11 4639 12 0061 12 5779 13 1808 13 8164 14 4866 15 1929 15 9374 167220 17 5487 18 4197 19 3373 20 3637 213215 22 3931 23 5213 247089 259927 11 11 5668 12 1687 12 8078 13 464 14 2068 149716 15 7836 16 6455 17 5603 18 5312 19414 205546 218143 23 0445 243493 25 7329 27 1999 28 7551 30 4035 22 1504 12126825 13 4121 14 1920 15 0258 159171168699 17 8885 18 977120 1407 21 3843 22 7132 241331 25 5502 27 2707 29 0017 30 8502 32 8229 349311 37 1802 39 5805 13 13 8093 14 6803 1 56178 166268 177130 18 8821 201406 21 4953 22 9534 24 5227 26 2116 28 0291 29 9847 32 0887 343519 36 7862 39 4000 47 2187 45 2445 14 14 9474 159739 17 0863 18 2919 19 5986 21 0151 22 5505 24 2149 26 0192 27 9750 30 0949 32 3926 348827 37 5811 40 5047 43 6720 47  1027 508180 54 8409 59 1959 15 16 0969172934 18 5989 200236 215786 23 2760 25 1290 27 1521 29 3609 31 7725 34 4054 37 2797 40 4175 3 8424 47 5804 51 6595 56  1101 60 9653 66 2607 720351 16 17 2579 186393 20 1569218245 25575 256725278881 30 3243 33 0034 35 9497 39 1899 42 7533 166717 50 9804 55 7175 60 9250 66 5488 72 9390 18502 17 18 4304 200121 21 7616 2369755 8404 282129308402 33 7502 5 9737 40547 TOOR 88837 53 7391 59 1176 65 0751 71 6730 789791 370680 960217 1059306 18 19 6147 214123 23 4144256454 28 1324 309057 33 9990 37 450241 3013 45 5992 50 3959 55 7497 61 7251 68 3961 75 8364 841402 93 4056 103 7403 115 2659 128 1167 19 208109228406 25 1169 276712 30 539033 7600 37 3790 41 4463 460185 511591 56 939 634397 70 7494 789692 88 2118 986032 110 2846 1234135 138 1664 154 7400 20 22 0190 24 2974 268704 297781 330660 36 7856 409955 45 7620511601 57 2750 642078720524 809468 910249102 4436 1153797 30 0329166280 165 4180 186 6880 21 23 2392 25 7833 286765 319692 35 7193 39 9927 448652 50 422956 7645 540025 72 2651 816987 92 46991047684 118 8101 134 8405 152 1385170210 197 81742750256 22 24 4716 27 2990 30 5368 342680 3850524392349 0057 55 4568 628733 714027 81 21 92 5006 105 610 120 4360 1376316 157 4150 1801721206 348 236 4384 271 0307 23 257163 288450 32 4529356179 414305 66 958 53 4361 60 8933695319 725830 91 16 1046019 120 2018 138910 1592764 53 6014 211 301324448682023518 326 2368 24 269735304219 344265 390826 445020 50 8156 58 1767 380973702 1741 18 1552 1368315 1586556 1341678 213 976 28 8075 2894945 3370105 3926542 25 28242320303 36 4593 416459 47 7271 518645 63 2490 73 1059347003 983471 1144133 133 33391556196 181 8708 212 7930 249 21402 92 101 42 6035 4020424 471 9811 26 29 5256 336709 111 38 5530 43117 68 6765 51 1135 79 9544 9111100118 58 1564 1503339 176 8501 208 3327 245 7120 567 3773 2900883 312 7626 4052721 4794305 308209 35343 40 7096 70M2 546691 61 705374 418 87 350 272 11 1 0 10 2003406 238 1993 283 5638 337 5024 681 8527 40203234792211 571 5223 32 1291 429309 370512 39676 584026 685281 5 38 1126 1 0 4723718 17 327 1041 392 5027 566 4808 681 1116 819 7233 33 45048722 452188 59063 3227 7368 7365103 565914151 61) 11 585311 312 313721697 4563032 552 5120 669 4474 8115228 8 113 837 136 135 34784940568175754 5609 643890587 1 1 9678341451 530 311 647 4350 7909479 9567121 115132 57313176701 10488864604020 754013502551079815476701926351398056537 101101005 1773090 5529 829 2350 75731345224163212 7343 856 10 11279691526671 30334807503359406 5289737701 8150816VOR M 50614632845794 IN S A 7 212 714 10056515089 50 21813 09 3151533 45497 17 Future Value of a Single Amount ($1 at the End of n Periods) (Used to compute the Compounded Future Value of a Known Lump Sum) 8  9  10  129 134 7  10700 1 000 1 0900 1 100 1 1100 1 1200 1 1300 1 1449 1 1664 1 1881 1 2100 n 1 2 3 4 5 1221 1 2544 1 2769 1 2597 1 2950 14049 14429 1 2250 13108 14026 13605 1 4116 1 5181 1 5735 16305 14683 1 5396 1 9254 1 5869 16771 18704 2 0820 1 5007 16058 1 9738 2 2107 1 7138 18280 2 0762 2 3526 17182 1 8909 19926 24760 2 6584 9 18385 1990 21719 23674 2 5931 2 7731 3 1058 3 4785 38960 3 0040 3 3946 3 8359 28531 2 5804 28127 3 1384 43345 11 12 13 14 15 1 9672 2 1589 2 1049 23316 2 2522 2 5182 2 4098 27196 2 5785 29372 2 75903 1722 229522 34259 3 4523 43535 4 8980 3 0658 33417 1  2  3  4  5  6  1 0100 10200 1 0300 1 000 1 0500 10600 1 0201 10404 1 0609 1 0816 1 1025 1 1236 1 0303 1 0612 1 0927 1 1249 1 1576 1 1910 1 0406 10824 1 1255 1 1699 1 2155 12625 10510 1 1041 1 1993 1 2167 1 276 13382 1 0615 1 1262 1 1941 1 2653 1 3401 14185 10721 1 1487 1 2299 13159 1 4071 1 5036 1 0829 1 1717 1 2668 1 3686 1 4775 1 5938 10937 1 1951 13048 1 4233 1 5513 16995 1 1046 1 2190 13439 1 4802 1 6289 1 7908 1 1157 1 2434 13842 1 5395 1 7103 18983 1 1268 1 2682 14258 16010 1 1959 20122 1 1381 12936 14685 16651 1 8856 2 1329 1 1495 1 3195 15126 1 73171 9799 2 2609 1 1610 1 3459 15580 1 8009 2 0789 23966 1 1726 1 3728 16047 1 87302 1829 2 5404 1 1843 1 4002 16528 1 9479 2 2920 26928 1 1961 1 4282 1 7024 2 0258 2 4066 28543 1 2081 14568 1 7535 2 1068 2 5270 30256 1 2202 14859 18061 2 1911 2 65333 2071 1 2324 15157 18603 2 2788 27860 33996 1 9161 2 3699 2 9253 36035 1 2572 15769 19736 2 464730715 38197 2 0328 2 5633 3 2251 40689 16406 2 0938 2 6658 3 386642919 2 1566 2 7725 3 5557 45494 1308217069 2221388343 733548223 13213 1 7410 22879 29987 3 9201 5 1117 1 7758 23566 3 1187 4 1161 54184 B114 24273 3 2434 4321957435 22080 32620 48010 70100 102857 15446 2 6916 4389 71057 11 4674 184202 3 6425 3 7975 4 1772 4 5950 4 8871 5 4736 6,1304 5 5348 6 2543 7 0673 14  15  16  17  18  19  20  1 1400 1 1500 1 1600 1 1700 1 1800 1 1900 2000 1 2996 13225 1 3456 13689 1 39 24 1 4161 1 4400 1 4815 15209 1 5609 1 6016 1 6430 1 6852 1 7280 1 6890 1 7490 18106 18739 1 9388 2 0093 20736 2 0114 2 1003 2 1924 2 7878 23864 26883 2 1950 2 3131 2 4364 2 5652 2 6996 2 8398 2 9860 25023 2 6600 2 8262 30012 3 1855 33793 35832 2 8526 3 0590 3 7784 3 5115 3 7509 40214 42998 3 2519 3 5179 2030 4 1084 4 7854 5 1598 3 7072 4 0456 4,4114 48068 5 2338 5 6947 6 1917 4 2262 4 6524 5 1173 56240 6 1759 6 7767 7 801 4 8179 5 3503 5 9360 65801 72876 8 0542 9161 5 4934 6 1528 6 8858 76987 8 5994 9 5964 10 6993 6 2613 7 0757 7 9875 9 0075 10 1472 11 4198 12 8392 7 1379 8 1371 9 2655 10 5387 11 9737 13 5895 154070 8 1372 9 3576 107480 12 3303 141290 16 1715 18 6884 9 2765 10 7613 12 4677 14,4265 16 6722 19 2441 22 1861 10 5752 123755 14 4625 16 8790 19 6733 22 9005 26 6233 12 0557 14 2318 16 7765 197484 23 2144 27 2516 319480 13 7435 163665 19 4608 23 1056 27 3930 32 4294 383376 15 626 18 3215 22 5745 270336 323238 38 5910 46 0051 17 3510 21 6447 26  1864 316293 38 1421 45 9233 55 2061 20 36 16 24 8915 303762 3700624 5 0076 546487 66 2474 28 6252 35 2361 3 2973 53 1090 65 0320 79 4968 32 9190 40 8742 506578 62 6686 77 3881 95 3962 47 4141 59 2697 73 9490 92 0918 114 4755 13 5353 550004 593455 87 2598 109 5893373706 50 0656 63 2004 81 1342 102 9566 130 4112 164 8147 57 5755 740085 949271 121 5005 155 189 197 8136 1110647 1433706184 6753 2373763 67 5635 378 7212 5338587 75037831051668 1469772 2330 1030 657 1670 704256615 392735759889149100438 53101 39703 43276 17 3 1583 3 7000 58951 6 8660 50545 5 5599 3 3799 3 9960 4 7171 6 9436 7 6900 7 9861 9 0243 10 1974 361654 3157 5 1417 6 1159 72633 86128 96453 38697 56044 6 7225 11 5231 46610 50338 4 1405 6 1088 10 8038 130211 4430454365 6 6586 12 1003 14,7138 7905 5871572579 110253 13 5523 15 1285 86231 50724 6341 79111 54274 68085 58074 7 394 93992 6213979851 102051 65688 6271 111671 71143 9 3173 12 1722 76123100627 13 7677 149745 217245 314094 294570 46 9016 743575 1400 117 30 RUN THE NUMBERS When You Should Refinance Your Mortgage It is sometimes advantageous to refinance an existing mortgage when interest rates dedine  In mortgage refinancing, a new mortgage is obtained to pay off and replace an existing mortgage  Most often it is undertaken to lower the monthly payment on the home by taking out a new loan with a lower interest rate  The example here illustrates how to determine whether refinancing your mortgage is a wise choice  The original mortgage for $160,000 was obtained seven years ago at a 5 5 percent interest rate for 30 years  The monthly pay  ment is $908  After seven years, the principal owed has declined to $142,100  If interest rates for new mortgages have declined to 4 5 percent, the owner could take out a new mortgage at the lower rate for a monthly payment of $827  Borrowing $142,100 for 23 years at 4 5 percent saves approximately 581 per month (5908   $827)  How ever, refinancing may have some up front costs, including a possible prepayment penalty on the old mort  gage and closing costs for the new mortgage  The question then becomes, will these costs exceed the monthly savings gained with a DO IT IN CLASS lower payment  The following worksheet provides a means for estimat  ing whether refinancing offers an advantage  It compares the future value of the reduced monthly payments (line 5) with the future value of the money used to pay the up front costs (estimated here at 2 ) of refinancing (line 8)  The homeowner would need to estimate the number of months he or she ex  pects to own the home after refinancing  Given an estimate of four years in this example, the net savings would be $977 (sub  tracting line 8 from line 5), and refinancing would benefit the owner  In this example, planning to live in the home only three more years would result in it not being financially advantageous to refinance  A similar worksheet can be found at www bankrate com calculators mortgages refinance calculator aspx Your Figures Example $908 827 81 4,175 Decision Factors 1  Current monthly payment 2  New monthly payment 3  Monthly savings (line 1   line 2) 4  Additional years you expect to live in the house 5  Future value of an account balance after 4 years if the monthly savings were invested at 3  after taxes (using the calculator on the Garman Forgue companion website) 6  Prepayment penalty on current loan (0 ) 7  Points and fees for new loan (2 ) 8  Future value of an account balance after 4 years if the prepayment penalty and closing costs (54,263) had been invested instead at 3  after taxes (using the calculator on the Garman Forgue companion website) 9  Net saving after 48 months dine 5   line 8) 2,842 3,198 $977 It may also be possible to borrow more than the current balance owed on the existing loan, thereby utilizing some of the equity built up in the home Borrowers refinancing for more than the amount owed should understand that rebuilding the equity to its previous level may take many years  This also is dangerous because if home prices decline the borrower will owe more on the home than it is worth Table 9 4 Estimating Mortgage Loan Payments for Principal and Interest (Monthly Payment per $1,000 Borrowed) 5 5 Payment Period (Years) Interest Rate ( ) 15 20 25 30 3 0 $6 9058 $5 5460 $4 7421 $4 2160 3 5 7 1488 5 7996 5 0062 4 4904 4 0 7 3969 6 0598 5 2783 4 7742 4 5 7 6499 6 3265 5 5583 5 0669 5 0 7 9079 6 5996 5 8459 5 3682 8 1708 6 8789 6 1409 5 6779 6 0 8 4386 7 1643 6 4430 5 9955 6 5 8 7111 7 4557 6 7521 6 3207 7 0 8 9883 7 7530 7 0678 6 6530 7 5 9 2701 8 0559 7 3899 6 9921 8 0 9 5565 8 3644 Note  To use this table to figure a monthly mortgage payment, divide the amount borrowed by 1,000 and multiply by the 7 7182 7  3376 ppropriate figure in the table for the interest rate and time period of the loan  For example, a 5160,000 loan for 30 years 60 percent would require a payment of $959,280 (5160,000    1,000) X 5 9955), over 20 years, it would require a ayment of $1,146 29 (5160,000   1,000) X 7 1643  For calculations for different interest rates, visit the Garman Forgue ompanion website

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Do the Math 9-4 Refinancing a Mortgage Kevin Tutumbo of Terre Haute, Indiana, has owned his home for 15 years and expects to live in

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