A sailboat costs $30,568. You pay 20% down and amortize the rest with equal monthly payments...

A sailboat costs $30,568. You pay 20% down and amortize the rest with equal monthly payments over a 10-year period. If you must pay 6.6% compounded monthly, what is your monthly payment? How much interest will you pay?

Expert Solution

Sailboat Costs	$ 30568
Down payment 20%	$ 6113.60

Loan amount	$ 24454.40
Rate of interest	6.60%
Loan tenor (in years)	10

Annuity factor can be calculated using below formula:

Annuity factor = [(1/r)-{(1/r)*(1/ (1+r)^t)}]

Where, r = periodic interest rate

t = total number of payments

Monthly payment = Loan amount / Annuity factor

For this case:

If laon to be paid out at monthly inetrvals:	12 times a year
periodic interest rate (r)	0.55%
tenor (t)	120
Annuity factor	87.67512
Monthly cash payment	$ 278.9206
Annual cash outflow	$ 3347.048
Total Cash outlow	$ 33470.48

Total Interest paid	$ 9016.08

The detail calculation is as below:

Number of pay out	Balance at beginning of payment	Interest	Monthly payment	Amortisation of loan	Balance at end of payment
1	24454.40	134.50	278.92	144.42	24309.98
2	24309.98	133.70	278.92	145.22	24164.76
3	24164.76	132.91	278.92	146.01	24018.75
4	24018.75	132.10	278.92	146.82	23871.93
5	23871.93	131.30	278.92	147.63	23724.31
6	23724.31	130.48	278.92	148.44	23575.87
7	23575.87	129.67	278.92	149.25	23426.62
8	23426.62	128.85	278.92	150.07	23276.54
9	23276.54	128.02	278.92	150.90	23125.64
10	23125.64	127.19	278.92	151.73	22973.91
11	22973.91	126.36	278.92	152.56	22821.35
12	22821.35	125.52	278.92	153.40	22667.94
13	22667.94	124.67	278.92	154.25	22513.70
14	22513.70	123.83	278.92	155.10	22358.60
15	22358.60	122.97	278.92	155.95	22202.65
16	22202.65	122.11	278.92	156.81	22045.85
17	22045.85	121.25	278.92	157.67	21888.18
18	21888.18	120.38	278.92	158.54	21729.64
19	21729.64	119.51	278.92	159.41	21570.24
20	21570.24	118.64	278.92	160.28	21409.95
21	21409.95	117.75	278.92	161.17	21248.79
22	21248.79	116.87	278.92	162.05	21086.73
23	21086.73	115.98	278.92	162.94	20923.79
24	20923.79	115.08	278.92	163.84	20759.95
25	20759.95	114.18	278.92	164.74	20595.21
26	20595.21	113.27	278.92	165.65	20429.56
27	20429.56	112.36	278.92	166.56	20263.00
28	20263.00	111.45	278.92	167.47	20095.53
29	20095.53	110.53	278.92	168.40	19927.14
30	19927.14	109.60	278.92	169.32	19757.81
31	19757.81	108.67	278.92	170.25	19587.56
32	19587.56	107.73	278.92	171.19	19416.37
33	19416.37	106.79	278.92	172.13	19244.24
34	19244.24	105.84	278.92	173.08	19071.16
35	19071.16	104.89	278.92	174.03	18897.14
36	18897.14	103.93	278.92	174.99	18722.15
37	18722.15	102.97	278.92	175.95	18546.20
38	18546.20	102.00	278.92	176.92	18369.28
39	18369.28	101.03	278.92	177.89	18191.39
40	18191.39	100.05	278.92	178.87	18012.53
41	18012.53	99.07	278.92	179.85	17832.67
42	17832.67	98.08	278.92	180.84	17651.83
43	17651.83	97.09	278.92	181.84	17470.00
44	17470.00	96.08	278.92	182.84	17287.16
45	17287.16	95.08	278.92	183.84	17103.32
46	17103.32	94.07	278.92	184.85	16918.47
47	16918.47	93.05	278.92	185.87	16732.60
48	16732.60	92.03	278.92	186.89	16545.71
49	16545.71	91.00	278.92	187.92	16357.79
50	16357.79	89.97	278.92	188.95	16168.84
51	16168.84	88.93	278.92	189.99	15978.84
52	15978.84	87.88	278.92	191.04	15787.81
53	15787.81	86.83	278.92	192.09	15595.72
54	15595.72	85.78	278.92	193.14	15402.57
55	15402.57	84.71	278.92	194.21	15208.37
56	15208.37	83.65	278.92	195.27	15013.09
57	15013.09	82.57	278.92	196.35	14816.75
58	14816.75	81.49	278.92	197.43	14619.32
59	14619.32	80.41	278.92	198.51	14420.80
60	14420.80	79.31	278.92	199.61	14221.20
61	14221.20	78.22	278.92	200.70	14020.49
62	14020.49	77.11	278.92	201.81	13818.68
63	13818.68	76.00	278.92	202.92	13615.77
64	13615.77	74.89	278.92	204.03	13411.73
65	13411.73	73.76	278.92	205.16	13206.58
66	13206.58	72.64	278.92	206.28	13000.29
67	13000.29	71.50	278.92	207.42	12792.87
68	12792.87	70.36	278.92	208.56	12584.31
69	12584.31	69.21	278.92	209.71	12374.61
70	12374.61	68.06	278.92	210.86	12163.75
71	12163.75	66.90	278.92	212.02	11951.73
72	11951.73	65.73	278.92	213.19	11738.54
73	11738.54	64.56	278.92	214.36	11524.18
74	11524.18	63.38	278.92	215.54	11308.64
75	11308.64	62.20	278.92	216.72	11091.92
76	11091.92	61.01	278.92	217.92	10874.01
77	10874.01	59.81	278.92	219.11	10654.89
78	10654.89	58.60	278.92	220.32	10434.57
79	10434.57	57.39	278.92	221.53	10213.04
80	10213.04	56.17	278.92	222.75	9990.29
81	9990.29	54.95	278.92	223.97	9766.32
82	9766.32	53.71	278.92	225.21	9541.11
83	9541.11	52.48	278.92	226.44	9314.67
84	9314.67	51.23	278.92	227.69	9086.98
85	9086.98	49.98	278.92	228.94	8858.04
86	8858.04	48.72	278.92	230.20	8627.84
87	8627.84	47.45	278.92	231.47	8396.37
88	8396.37	46.18	278.92	232.74	8163.63
89	8163.63	44.90	278.92	234.02	7929.61
90	7929.61	43.61	278.92	235.31	7694.30
91	7694.30	42.32	278.92	236.60	7457.70
92	7457.70	41.02	278.92	237.90	7219.79
93	7219.79	39.71	278.92	239.21	6980.58
94	6980.58	38.39	278.92	240.53	6740.05
95	6740.05	37.07	278.92	241.85	6498.20
96	6498.20	35.74	278.92	243.18	6255.02
97	6255.02	34.40	278.92	244.52	6010.51
98	6010.51	33.06	278.92	245.86	5764.64
99	5764.64	31.71	278.92	247.22	5517.43
100	5517.43	30.35	278.92	248.57	5268.85
101	5268.85	28.98	278.92	249.94	5018.91
102	5018.91	27.60	278.92	251.32	4767.59
103	4767.59	26.22	278.92	252.70	4514.90
104	4514.90	24.83	278.92	254.09	4260.81
105	4260.81	23.43	278.92	255.49	4005.32
106	4005.32	22.03	278.92	256.89	3748.43
107	3748.43	20.62	278.92	258.30	3490.12
108	3490.12	19.20	278.92	259.72	3230.40
109	3230.40	17.77	278.92	261.15	2969.25
110	2969.25	16.33	278.92	262.59	2706.66
111	2706.66	14.89	278.92	264.03	2442.62
112	2442.62	13.43	278.92	265.49	2177.14
113	2177.14	11.97	278.92	266.95	1910.19
114	1910.19	10.51	278.92	268.41	1641.78
115	1641.78	9.03	278.92	269.89	1371.88
116	1371.88	7.55	278.92	271.38	1100.51
117	1100.51	6.05	278.92	272.87	827.64
118	827.64	4.55	278.92	274.37	553.27
119	553.27	3.04	278.92	275.88	277.39
120	277.39	1.53	278.92	277.39	0.00

jeff jeffy answered 1 year ago

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