Question

Holly received a loan of $36,000 at 3.5% compounded monthly. She had to make payments at the end of every month for a period of 5 years to settle the loan. a. Calculate the size of payments. 0.00 Round to the nearest cent

b. Fill in the partial amortization schedule for the loan, rounding your answers to two decimal places.

Answer 1

a)	Size of Payments are $654.90 Size of payment = P*r*(1+r)n / {(1+r)n - 1} where, P = Principal ( Amonut Borrowed) r = interest rate/12 n = term (number of payments) = 5 Year * 12 Months = 60 Months By applying the above formula Size of payments = 36000*.035/12(1+.035/12)60 / {(1+.035/12)60 - 1}    = $654.90
b)	Partial amortization schedule for the loan
Payment Number (1)	Payment (2)	Interest Portion (3)	Principal Portion (4 = 2-3)	Principal Balance (5)
0				$ 36,000.00
1	$        654.90	$     105.00	$        549.90	$ 35,450.10
2	$        654.90	$     103.40	$        551.50	$ 34,898.60
3	$        654.90	$     101.79	$        553.11	$ 34,345.48
4	$        654.90	$     100.17	$        554.73	$ 33,790.76
5	$        654.90	$        98.56	$        556.34	$ 33,234.41
6	$        654.90	$        96.93	$        557.97	$ 32,676.45
7	$        654.90	$        95.31	$        559.59	$ 32,116.85
8	$        654.90	$        93.67	$        561.23	$ 31,555.63
9	$        654.90	$        92.04	$        562.86	$ 30,992.77
10	$        654.90	$        90.40	$        564.50	$ 30,428.26
11	$        654.90	$        88.75	$        566.15	$ 29,862.11
12	$        654.90	$        87.10	$        567.80	$ 29,294.31
13	$        654.90	$        85.44	$        569.46	$ 28,724.85
14	$        654.90	$        83.78	$        571.12	$ 28,153.73
15	$        654.90	$        82.12	$        572.78	$ 27,580.95
16	$        654.90	$        80.44	$        574.46	$ 27,006.49
17	$        654.90	$        78.77	$        576.13	$ 26,430.36
18	$        654.90	$        77.09	$        577.81	$ 25,852.55
19	$        654.90	$        75.40	$        579.50	$ 25,273.05
20	$        654.90	$        73.71	$        581.19	$ 24,691.86
21	$        654.90	$        72.02	$        582.88	$ 24,108.98
22	$        654.90	$        70.32	$        584.58	$ 23,524.40
23	$        654.90	$        68.61	$        586.29	$ 22,938.11
24	$        654.90	$        66.90	$        588.00	$ 22,350.12
25	$        654.90	$        65.19	$        589.71	$ 21,760.40
26	$        654.90	$        63.47	$        591.43	$ 21,168.97
27	$        654.90	$        61.74	$        593.16	$ 20,575.81
28	$        654.90	$        60.01	$        594.89	$ 19,980.93
29	$        654.90	$        58.28	$        596.62	$ 19,384.30
30	$        654.90	$        56.54	$        598.36	$ 18,785.94
31	$        654.90	$        54.79	$        600.11	$ 18,185.83
32	$        654.90	$        53.04	$        601.86	$ 17,583.98
33	$        654.90	$        51.29	$        603.61	$ 16,980.36
34	$        654.90	$        49.53	$        605.37	$ 16,374.99
35	$        654.90	$        47.76	$        607.14	$ 15,767.85
36	$        654.90	$        45.99	$        608.91	$ 15,158.94
37	$        654.90	$        44.21	$        610.69	$ 14,548.25
38	$        654.90	$        42.43	$        612.47	$ 13,935.79
39	$        654.90	$        40.65	$        614.25	$ 13,321.53
40	$        654.90	$        38.85	$        616.05	$ 12,705.49
41	$        654.90	$        37.06	$        617.84	$ 12,087.64
42	$        654.90	$        35.26	$        619.64	$ 11,468.00
43	$        654.90	$        33.45	$        621.45	$ 10,846.55
44	$        654.90	$        31.64	$        623.26	$ 10,223.28
45	$        654.90	$        29.82	$        625.08	$    9,598.20
46	$        654.90	$        27.99	$        626.91	$    8,971.30
47	$        654.90	$        26.17	$        628.73	$    8,342.56
48	$        654.90	$        24.33	$        630.57	$    7,711.99
49	$        654.90	$        22.49	$        632.41	$    7,079.59
50	$        654.90	$        20.65	$        634.25	$    6,445.34
51	$        654.90	$        18.80	$        636.10	$    5,809.24
52	$        654.90	$        16.94	$        637.96	$    5,171.28
53	$        654.90	$        15.08	$        639.82	$    4,531.46
54	$        654.90	$        13.22	$        641.68	$    3,889.78
55	$        654.90	$        11.35	$        643.55	$    3,246.22
56	$        654.90	$          9.47	$        645.43	$    2,600.79
57	$        654.90	$          7.59	$        647.31	$    1,953.48
58	$        654.90	$          5.70	$        649.20	$    1,304.28
59	$        654.90	$          3.80	$        651.10	$        653.18
60	$        654.90	$          1.91	$        653.18	$            0.00
Total:	$ 39,294.00	$ 3,294.18	$ 36,000.00

Calculation of partial amortisation schedule of 1st payment is as follows:

Payment = $654.90 (as calculated above in part "a")

Interest = Principal at the begning of the period * r

where, r = i/12

Now interest = $36000 * .035/12

   = $105

Accordingly,

Principal portion = Size of Payment - Interest Portion

   = $654.9 - $105

   = $549.90

So the principal balance after first payment is

Principal at the begning - Principal paid

=$36,000 - $549.90

=$35450.10

Accordingly we can calculate the above amortization schedule