document.write( "Question 384063: I greatly NEED some help URGENTLY with this problem. i tried to do it forever but i dont get it so would somebody PLEASE HELP ME! I REALLY NEED A QUICK ANSWER. THANK YOU!
\n" ); document.write( "Lesson 4—4
\n" ); document.write( "Two loan balances can be approximated by the equations given in the table. The time x is in years. i will separate things in table with a (/)\r
\n" ); document.write( "\n" ); document.write( "Loan Amount / Interest rate / Years / Equation\r
\n" ); document.write( "\n" ); document.write( "$200,000 / 7% / 20 yrs / y= -9,734.7x + 218,761
\n" ); document.write( "$250,000 / 6.25% / 15 yrs / y= -16,474x + 266,478
\n" ); document.write( "
\n" ); document.write( "1)Use Matrices and the inverse matrix to find when the loan balances will be approximately the same for the two loans before the final payment is made.
\n" ); document.write( "2)What will the approximate balance of each loan be at that time?
\n" ); document.write( "3)Why might your estimate of the time when the loan balances will be the same be somewhat inaccurate?
\n" ); document.write( "THANK YOU SO MUCH IN ADVANCE!
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #271855 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
The 2 equations that approximate the solution to this are:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "y = -9734.7 * x + 218,761\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "y = -16474 * x + 266,478\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you graph both these equations, you will see when they cross.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The graph of both of these equations is shown below:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You can see from the graph that the approximate intersection point is somewhere around 7 years.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You can calculate that by making the equations equal to each other.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "When you do that, you are saying that the value of y in the first equation is equal to the value of y in the second equation.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "you get:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-9734.7x + 218761 = -16474 * x + 266,478\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solve this equation algebraically to get an answer of:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "x = 7.080408945
\n" ); document.write( "y = 149835.343\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The approximation given by the graph is pretty close.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "x is the number of years when the balances will be approximately equal.
\n" ); document.write( "y i the outstanding balance in each account at that time.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The estimate will be somewhat inaccurate because the declining balance equation is not a straight line.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "What the equations show are probability the best fit of a straight line to the actual balances as they drop in time.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The actual point where the balances are equal can be calculated through the use of Present Value of A Loan Amount Formulas, or through the use of a mechanized program that will do the calculations for each year of each loan.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I used Excel to do that for you, after having calculated what the monthly payments would be using a financial calculator, and the results are shown below:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "	Remaining Balance		\r\n" );
document.write( "year	Loan1	Loan2	\r\n" );
document.write( "0	$200,000.00	$250,000.00	\r\n" );
document.write( "1	$199,616.07 	$249,158.53 	\r\n" );
document.write( "2	$199,229.90 	$248,312.67 	\r\n" );
document.write( "3	$198,841.47 	$247,462.41 	\r\n" );
document.write( "4	$198,450.79 	$246,607.72 	\r\n" );
document.write( "5	$198,057.82 	$245,748.58 	\r\n" );
document.write( "6	$197,662.56 	$244,884.96 	\r\n" );
document.write( "7	$197,264.99 	$244,016.84 	\r\n" );
document.write( "8	$196,865.10 	$243,144.21 	\r\n" );
document.write( "9	$196,462.89 	$242,267.03 	\r\n" );
document.write( "10	$196,058.32 	$241,385.28 	\r\n" );
document.write( "11	$195,651.40 	$240,498.93 	\r\n" );
document.write( "12	$195,242.10 	$239,607.98 	\r\n" );
document.write( "13	$194,830.41 	$238,712.38 	\r\n" );
document.write( "14	$194,416.33 	$237,812.11 	\r\n" );
document.write( "15	$193,999.82 	$236,907.16 	\r\n" );
document.write( "16	$193,580.89 	$235,997.50 	\r\n" );
document.write( "17	$193,159.52 	$235,083.09 	\r\n" );
document.write( "18	$192,735.68 	$234,163.93 	\r\n" );
document.write( "19	$192,309.38 	$233,239.97 	\r\n" );
document.write( "20	$191,880.58 	$232,311.21 	\r\n" );
document.write( "21	$191,449.29 	$231,377.60 	\r\n" );
document.write( "22	$191,015.48 	$230,439.14 	\r\n" );
document.write( "23	$190,579.14 	$229,495.79 	\r\n" );
document.write( "24	$190,140.25 	$228,547.52 	\r\n" );
document.write( "25	$189,698.80 	$227,594.31 	\r\n" );
document.write( "26	$189,254.78 	$226,636.14 	\r\n" );
document.write( "27	$188,808.17 	$225,672.98 	\r\n" );
document.write( "28	$188,358.95 	$224,704.81 	\r\n" );
document.write( "29	$187,907.12 	$223,731.59 	\r\n" );
document.write( "30	$187,452.64 	$222,753.30 	\r\n" );
document.write( "31	$186,995.52 	$221,769.91 	\r\n" );
document.write( "32	$186,535.73 	$220,781.41 	\r\n" );
document.write( "33	$186,073.26 	$219,787.75 	\r\n" );
document.write( "34	$185,608.09 	$218,788.92 	\r\n" );
document.write( "35	$185,140.20 	$217,784.89 	\r\n" );
document.write( "36	$184,669.59 	$216,775.63 	\r\n" );
document.write( "37	$184,196.23 	$215,761.11 	\r\n" );
document.write( "38	$183,720.11 	$214,741.31 	\r\n" );
document.write( "39	$183,241.21 	$213,716.20 	\r\n" );
document.write( "40	$182,759.52 	$212,685.75 	\r\n" );
document.write( "41	$182,275.02 	$211,649.93 	\r\n" );
document.write( "42	$181,787.69 	$210,608.72 	\r\n" );
document.write( "43	$181,297.52 	$209,562.08 	\r\n" );
document.write( "44	$180,804.50 	$208,509.99 	\r\n" );
document.write( "45	$180,308.59 	$207,452.42 	\r\n" );
document.write( "46	$179,809.79 	$206,389.35 	\r\n" );
document.write( "47	$179,308.09 	$205,320.74 	\r\n" );
document.write( "48	$178,803.45 	$204,246.56 	\r\n" );
document.write( "49	$178,295.87 	$203,166.78 	\r\n" );
document.write( "50	$177,785.34 	$202,081.39 	\r\n" );
document.write( "51	$177,271.82 	$200,990.34 	\r\n" );
document.write( "52	$176,755.31 	$199,893.60 	\r\n" );
document.write( "53	$176,235.78 	$198,791.16 	\r\n" );
document.write( "54	$175,713.23 	$197,682.97 	\r\n" );
document.write( "55	$175,187.62 	$196,569.02 	\r\n" );
document.write( "56	$174,658.95 	$195,449.25 	\r\n" );
document.write( "57	$174,127.20 	$194,323.66 	\r\n" );
document.write( "58	$173,592.34 	$193,192.21 	\r\n" );
document.write( "59	$173,054.37 	$192,054.86 	\r\n" );
document.write( "60	$172,513.25 	$190,911.59 	\r\n" );
document.write( "61	$171,968.98 	$189,762.36 	\r\n" );
document.write( "62	$171,421.53 	$188,607.15 	\r\n" );
document.write( "63	$170,870.90 	$187,445.92 	\r\n" );
document.write( "64	$170,317.05 	$186,278.65 	\r\n" );
document.write( "65	$169,759.96 	$185,105.29 	\r\n" );
document.write( "66	$169,199.63 	$183,925.82 	\r\n" );
document.write( "67	$168,636.03 	$182,740.21 	\r\n" );
document.write( "68	$168,069.14 	$181,548.43 	\r\n" );
document.write( "69	$167,498.95 	$180,350.44 	\r\n" );
document.write( "70	$166,925.43 	$179,146.20 	\r\n" );
document.write( "71	$166,348.56 	$177,935.70 	\r\n" );
document.write( "72	$165,768.33 	$176,718.89 	\r\n" );
document.write( "73	$165,184.72 	$175,495.74 	\r\n" );
document.write( "74	$164,597.70 	$174,266.23 	\r\n" );
document.write( "75	$164,007.25 	$173,030.31 	\r\n" );
document.write( "76	$163,413.36 	$171,787.95 	\r\n" );
document.write( "77	$162,816.01 	$170,539.12 	\r\n" );
document.write( "78	$162,215.17 	$169,283.79 	\r\n" );
document.write( "79	$161,610.83 	$168,021.92 	\r\n" );
document.write( "80	$161,002.96 	$166,753.48 	\r\n" );
document.write( "81	$160,391.55 	$165,478.43 	\r\n" );
document.write( "82	$159,776.57 	$164,196.74 	\r\n" );
document.write( "83	$159,158.00 	$162,908.37 	\r\n" );
document.write( "84	$158,535.82 	$161,613.29 	\r\n" );
document.write( "85	$157,910.02 	$160,311.47 	\r\n" );
document.write( "86	$157,280.56 	$159,002.87 	\r\n" );
document.write( "87	$156,647.43 	$157,687.45 	\r\n" );
document.write( "88	$156,010.61 	$156,365.18 	*\r\n" );
document.write( "89	$155,370.07 	$155,036.03 	*\r\n" );
document.write( "90	$154,725.80 	$153,699.95 	\r\n" );
document.write( "91	$154,077.77 	$152,356.92 	\r\n" );
document.write( "92	$153,425.96 	$151,006.88 	\r\n" );
document.write( "93	$152,770.35 	$149,649.82 	\r\n" );
document.write( "94	$152,110.91 	$148,285.69 	\r\n" );
document.write( "95	$151,447.63 	$146,914.45 	\r\n" );
document.write( "96	$150,780.47 	$145,536.08 	\r\n" );
document.write( "97	$150,109.43 	$144,150.52 	\r\n" );
document.write( "98	$149,434.47 	$142,757.75 	\r\n" );
document.write( "99	$148,755.57 	$141,357.72 	\r\n" );
document.write( "100	$148,072.71 	$139,950.40 	\r\n" );
document.write( "101	$147,385.87 	$138,535.75 	\r\n" );
document.write( "102	$146,695.03 	$137,113.73 	\r\n" );
document.write( "103	$146,000.15 	$135,684.31 	\r\n" );
document.write( "104	$145,301.22 	$134,247.44 	\r\n" );
document.write( "105	$144,598.21 	$132,803.09 	\r\n" );
document.write( "106	$143,891.10 	$131,351.22 	\r\n" );
document.write( "107	$143,179.87 	$129,891.78 	\r\n" );
document.write( "108	$142,464.49 	$128,424.74 	\r\n" );
document.write( "109	$141,744.93 	$126,950.06 	\r\n" );
document.write( "110	$141,021.18 	$125,467.71 	\r\n" );
document.write( "111	$140,293.21 	$123,977.63 	\r\n" );
document.write( "112	$139,560.99 	$122,479.79 	\r\n" );
document.write( "113	$138,824.49 	$120,974.14 	\r\n" );
document.write( "114	$138,083.71 	$119,460.66 	\r\n" );
document.write( "115	$137,338.60 	$117,939.29 	\r\n" );
document.write( "116	$136,589.14 	$116,410.00 	\r\n" );
document.write( "117	$135,835.31 	$114,872.75 	\r\n" );
document.write( "118	$135,077.09 	$113,327.49 	\r\n" );
document.write( "119	$134,314.44 	$111,774.18 	\r\n" );
document.write( "120	$133,547.34 	$110,212.78 	\r\n" );
document.write( "121	$132,775.77 	$108,643.25 	\r\n" );
document.write( "122	$131,999.70 	$107,065.54 	\r\n" );
document.write( "123	$131,219.10 	$105,479.61 	\r\n" );
document.write( "124	$130,433.94 	$103,885.43 	\r\n" );
document.write( "125	$129,644.21 	$102,282.94 	\r\n" );
document.write( "126	$128,849.87 	$100,672.11 	\r\n" );
document.write( "127	$128,050.90 	$99,052.89 	\r\n" );
document.write( "128	$127,247.26 	$97,425.23 	\r\n" );
document.write( "129	$126,438.94 	$95,789.10 	\r\n" );
document.write( "130	$125,625.90 	$94,144.44 	\r\n" );
document.write( "131	$124,808.12 	$92,491.22 	\r\n" );
document.write( "132	$123,985.57 	$90,829.39 	\r\n" );
document.write( "133	$123,158.22 	$89,158.90 	\r\n" );
document.write( "134	$122,326.05 	$87,479.71 	\r\n" );
document.write( "135	$121,489.02 	$85,791.78 	\r\n" );
document.write( "136	$120,647.11 	$84,095.05 	\r\n" );
document.write( "137	$119,800.29 	$82,389.49 	\r\n" );
document.write( "138	$118,948.52 	$80,675.05 	\r\n" );
document.write( "139	$118,091.79 	$78,951.67 	\r\n" );
document.write( "140	$117,230.06 	$77,219.32 	\r\n" );
document.write( "141	$116,363.31 	$75,477.95 	\r\n" );
document.write( "142	$115,491.49 	$73,727.50 	\r\n" );
document.write( "143	$114,614.60 	$71,967.94 	\r\n" );
document.write( "144	$113,732.58 	$70,199.22 	\r\n" );
document.write( "145	$112,845.43 	$68,421.28 	\r\n" );
document.write( "146	$111,953.09 	$66,634.09 	\r\n" );
document.write( "147	$111,055.56 	$64,837.58 	\r\n" );
document.write( "148	$110,152.78 	$63,031.72 	\r\n" );
document.write( "149	$109,244.74 	$61,216.45 	\r\n" );
document.write( "150	$108,331.40 	$59,391.73 	\r\n" );
document.write( "151	$107,412.74 	$57,557.51 	\r\n" );
document.write( "152	$106,488.72 	$55,713.73 	\r\n" );
document.write( "153	$105,559.30 	$53,860.35 	\r\n" );
document.write( "154	$104,624.47 	$51,997.31 	\r\n" );
document.write( "155	$103,684.18 	$50,124.58 	\r\n" );
document.write( "156	$102,738.41 	$48,242.08 	\r\n" );
document.write( "157	$101,787.11 	$46,349.79 	\r\n" );
document.write( "158	$100,830.27 	$44,447.64 	\r\n" );
document.write( "159	$99,867.85 	$42,535.58 	\r\n" );
document.write( "160	$98,899.82 	$40,613.56 	\r\n" );
document.write( "161	$97,926.14 	$38,681.53 	\r\n" );
document.write( "162	$96,946.77 	$36,739.44 	\r\n" );
document.write( "163	$95,961.70 	$34,787.23 	\r\n" );
document.write( "164	$94,970.88 	$32,824.86 	\r\n" );
document.write( "165	$93,974.28 	$30,852.27 	\r\n" );
document.write( "166	$92,971.86 	$28,869.40 	\r\n" );
document.write( "167	$91,963.60 	$26,876.20 	\r\n" );
document.write( "168	$90,949.46 	$24,872.63 	\r\n" );
document.write( "169	$89,929.40 	$22,858.61 	\r\n" );
document.write( "170	$88,903.39 	$20,834.11 	\r\n" );
document.write( "171	$87,871.39 	$18,799.06 	\r\n" );
document.write( "172	$86,833.38 	$16,753.42 	\r\n" );
document.write( "173	$85,789.31 	$14,697.12 	\r\n" );
document.write( "174	$84,739.15 	$12,630.11 	\r\n" );
document.write( "175	$83,682.86 	$10,552.33 	\r\n" );
document.write( "176	$82,620.41 	$8,463.74 	\r\n" );
document.write( "177	$81,551.77 	$6,364.26 	\r\n" );
document.write( "178	$80,476.89 	$4,253.85 	\r\n" );
document.write( "179	$79,395.74 	$2,132.45 	\r\n" );
document.write( "180	$78,308.28 	($0.00)	\r\n" );
document.write( "181	$77,214.48 		\r\n" );
document.write( "182	$76,114.30 		\r\n" );
document.write( "183	$75,007.71 		\r\n" );
document.write( "184	$73,894.65 		\r\n" );
document.write( "185	$72,775.11 		\r\n" );
document.write( "186	$71,649.03 		\r\n" );
document.write( "187	$70,516.39 		\r\n" );
document.write( "188	$69,377.13 		\r\n" );
document.write( "189	$68,231.24 		\r\n" );
document.write( "190	$67,078.65 		\r\n" );
document.write( "191	$65,919.35 		\r\n" );
document.write( "192	$64,753.28 		\r\n" );
document.write( "193	$63,580.41 		\r\n" );
document.write( "194	$62,400.70 		\r\n" );
document.write( "195	$61,214.10 		\r\n" );
document.write( "196	$60,020.59 		\r\n" );
document.write( "197	$58,820.11 		\r\n" );
document.write( "198	$57,612.63 		\r\n" );
document.write( "199	$56,398.10 		\r\n" );
document.write( "200	$55,176.50 		\r\n" );
document.write( "201	$53,947.76 		\r\n" );
document.write( "202	$52,711.86 		\r\n" );
document.write( "203	$51,468.75 		\r\n" );
document.write( "204	$50,218.38 		\r\n" );
document.write( "205	$48,960.73 		\r\n" );
document.write( "206	$47,695.73 		\r\n" );
document.write( "207	$46,423.36 		\r\n" );
document.write( "208	$45,143.56 		\r\n" );
document.write( "209	$43,856.30 		\r\n" );
document.write( "210	$42,561.53 		\r\n" );
document.write( "211	$41,259.21 		\r\n" );
document.write( "212	$39,949.29 		\r\n" );
document.write( "213	$38,631.73 		\r\n" );
document.write( "214	$37,306.49 		\r\n" );
document.write( "215	$35,973.51 		\r\n" );
document.write( "216	$34,632.76 		\r\n" );
document.write( "217	$33,284.18 		\r\n" );
document.write( "218	$31,927.74 		\r\n" );
document.write( "219	$30,563.39 		\r\n" );
document.write( "220	$29,191.08 		\r\n" );
document.write( "221	$27,810.76 		\r\n" );
document.write( "222	$26,422.39 		\r\n" );
document.write( "223	$25,025.93 		\r\n" );
document.write( "224	$23,621.31 		\r\n" );
document.write( "225	$22,208.51 		\r\n" );
document.write( "226	$20,787.46 		\r\n" );
document.write( "227	$19,358.12 		\r\n" );
document.write( "228	$17,920.45 		\r\n" );
document.write( "229	$16,474.38 		\r\n" );
document.write( "230	$15,019.89 		\r\n" );
document.write( "231	$13,556.90 		\r\n" );
document.write( "232	$12,085.39 		\r\n" );
document.write( "233	$10,605.29 		\r\n" );
document.write( "234	$9,116.56 		\r\n" );
document.write( "235	$7,619.14 		\r\n" );
document.write( "236	$6,112.98 		\r\n" );
document.write( "237	$4,598.05 		\r\n" );
document.write( "238	$3,074.27 		\r\n" );
document.write( "239	$1,541.61 		\r\n" );
document.write( "240	$0.00 		\r\n" );
document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The asterisks (*) show you that the balances become equal somewhere between the 88th and 89th month.\r
\n" ); document.write( "\n" ); document.write( "This would be somewhere between 7.33333333 years and 7.41666666667 years.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The actual graph of the declining balance is not a straight line.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It drops slowly in the early years and drops a lot faster in the later years.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You can link to the following webiter and scroll down to the bottom and a graph of a remaining balance on a loan will show up.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You can see that it is not a straight line.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "http://www.tvmcalcs.com/calculators/apps/excel_loan_amortization\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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