Question

Amortization Table. You wish to buy a $40,000 car. The bank can finance you with a 3-year loan at a 4 percent APR. If you make a $7,000 down payment on the purchase. What are the monthly payments on your loan? How much will you pay in interest each year? Show the amortization table (use monthly payments).

Answer 1

1)	Monthly payment	=	Loan amount	/	Present value of annuity of 1
		=	$       33,000	/	33.8707664
		=	$       974.29
	Working:
	Loan amount	=	$       40,000	-	$         7,000
		=	$       33,000
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.00333)^-36)/0.00333		i	=	4%/12	=	0.003333
		=	33.8707664		n	=	3*12	=	36
2)	Interest for the year:
	1	$       1,127.73
	2	$           697.34
	3	$           249.42
3)	Monthly amortization:
	Month end	Beginning loan	Interest	Monthly Payment	Reduction of loan	Ending Loan
		a	b=a*4%*1/12	c	d=c-b	e=a-d
	1	$     33,000.00	$       110.00	$       974.29	$       864.29	$     32,135.71
	2	$     32,135.71	$       107.12	$       974.29	$       867.17	$     31,268.54
	3	$     31,268.54	$       104.23	$       974.29	$       870.06	$     30,398.47
	4	$     30,398.47	$       101.33	$       974.29	$       872.96	$     29,525.51
	5	$     29,525.51	$          98.42	$       974.29	$       875.87	$     28,649.64
	6	$     28,649.64	$          95.50	$       974.29	$       878.79	$     27,770.84
	7	$     27,770.84	$          92.57	$       974.29	$       881.72	$     26,889.12
	8	$     26,889.12	$          89.63	$       974.29	$       884.66	$     26,004.46
	9	$     26,004.46	$          86.68	$       974.29	$       887.61	$     25,116.85
	10	$     25,116.85	$          83.72	$       974.29	$       890.57	$     24,226.28
	11	$     24,226.28	$          80.75	$       974.29	$       893.54	$     23,332.74
	12	$     23,332.74	$          77.78	$       974.29	$       896.52	$     22,436.23
	Total		$    1,127.73	$ 11,691.50	$ 10,563.77
	13	$     22,436.23	$          74.79	$       974.29	$       899.50	$     21,536.73
	14	$     21,536.73	$          71.79	$       974.29	$       902.50	$     20,634.22
	15	$     20,634.22	$          68.78	$       974.29	$       905.51	$     19,728.71
	16	$     19,728.71	$          65.76	$       974.29	$       908.53	$     18,820.18
	17	$     18,820.18	$          62.73	$       974.29	$       911.56	$     17,908.63
	18	$     17,908.63	$          59.70	$       974.29	$       914.60	$     16,994.03
	19	$     16,994.03	$          56.65	$       974.29	$       917.64	$     16,076.38
	20	$     16,076.38	$          53.59	$       974.29	$       920.70	$     15,155.68
	21	$     15,155.68	$          50.52	$       974.29	$       923.77	$     14,231.91
	22	$     14,231.91	$          47.44	$       974.29	$       926.85	$     13,305.06
	23	$     13,305.06	$          44.35	$       974.29	$       929.94	$     12,375.12
	24	$     12,375.12	$          41.25	$       974.29	$       933.04	$     11,442.07
	Total		$       697.34	$ 11,691.50	$ 10,994.16
	25	$     11,442.07	$          38.14	$       974.29	$       936.15	$     10,505.92
	26	$     10,505.92	$          35.02	$       974.29	$       939.27	$       9,566.65
	27	$       9,566.65	$          31.89	$       974.29	$       942.40	$       8,624.25
	28	$       8,624.25	$          28.75	$       974.29	$       945.54	$       7,678.70
	29	$       7,678.70	$          25.60	$       974.29	$       948.70	$       6,730.01
	30	$       6,730.01	$          22.43	$       974.29	$       951.86	$       5,778.15
	31	$       5,778.15	$          19.26	$       974.29	$       955.03	$       4,823.12
	32	$       4,823.12	$          16.08	$       974.29	$       958.21	$       3,864.90
	33	$       3,864.90	$          12.88	$       974.29	$       961.41	$       2,903.50
	34	$       2,903.50	$            9.68	$       974.29	$       964.61	$       1,938.88
	35	$       1,938.88	$            6.46	$       974.29	$       967.83	$           971.05
	36	$           971.05	$            3.24	$       974.29	$       971.05	$               0.00
	Total		$       249.42	$ 11,691.50	$ 11,442.07
	Sub-Total		$    2,074.49	$ 35,074.49	$ 33,000.00