Chapter 4, Problem 104P

To determine

Tabular Representation of the balance due, principal payment, and interest rate.

Answer to Problem 104P

Tabular Representation of the balance due, principal payment, and interest rate.

Explanation of Solution

Given information:

• Loan Amount - $900
• Time period − 1 years
• Rate of Interest − 6% per annum

• Capital Recovery Factor:

The capital recovery factor is used to find the uniform annual amount A of a uniform series from a known present worth at the given interest rate i. It is calculated as:

$A=P\left[\frac{i{(1+i)}^n}{{(1+i)}^n-1}\right]=P(A/P,i,n)$.

Calculation:

The loan amount is $18,000. The monthly payments are to be made, therefore, the rate of interest will be divided by 12, while the time period will be multiplied by 12.

$\begin{array}{l}RoI=(8\%)/12=0.067\%\\ Timeperiod=5\times 12=60\\ MonthlyPayment=P(A/P,i,n)=\$521.99\end{array}$

Based on this, following table can be calculated:

Months	Total Payment	Principal	Interest Rate	Opening Balance	Closing Balance
1	547.46	367.46	180.00	27000.00	26632.54
2	547.46	369.91	177.55	26632.54	26262.62
3	547.46	372.38	175.08	26262.62	25890.25
4	547.46	374.86	172.60	25890.25	25515.39
5	547.46	377.36	170.10	25515.39	25138.03
6	547.46	379.88	167.59	25138.03	24758.15
7	547.46	382.41	165.05	24758.15	24375.74
8	547.46	384.96	162.50	24375.74	23990.78
9	547.46	387.52	159.94	23990.78	23603.26
10	547.46	390.11	157.36	23603.26	23213.15
11	547.46	392.71	154.75	23213.15	22820.44
12	547.46	395.33	152.14	22820.44	22425.12
13	547.46	397.96	149.50	22425.12	22027.16
14	547.46	400.61	146.85	22027.16	21626.54
15	547.46	403.29	144.18	21626.54	21223.25
16	547.46	405.97	141.49	21223.25	20817.28
17	547.46	408.68	138.78	20817.28	20408.60
18	547.46	411.41	136.06	20408.60	19997.19
19	547.46	414.15	133.31	19997.19	19583.05
20	547.46	416.91	130.55	19583.05	19166.14
21	547.46	419.69	127.77	19166.14	18746.45
22	547.46	422.49	124.98	18746.45	18323.96
23	547.46	425.30	122.16	18323.96	17898.66
24	547.46	428.14	119.32	17898.66	17470.52
25	547.46	430.99	116.47	17470.52	17039.53
26	547.46	433.87	113.60	17039.53	16605.66
27	547.46	436.76	110.70	16605.66	16168.90
28	547.46	439.67	107.79	16168.90	15729.24
29	547.46	442.60	104.86	15729.24	15286.63
30	547.46	445.55	101.91	15286.63	14841.08
31	547.46	448.52	98.94	14841.08	14392.56
32	547.46	451.51	95.95	14392.56	13941.05
33	547.46	454.52	92.94	13941.05	13486.53
34	547.46	457.55	89.91	13486.53	13028.97
35	547.46	460.60	86.86	13028.97	12568.37
36	547.46	463.67	83.79	12568.37	12104.70
37	547.46	466.76	80.70	12104.70	11637.93
38	547.46	469.88	77.59	11637.93	11168.06
39	547.46	473.01	74.45	11168.06	10695.05
40	547.46	476.16	71.30	10695.05	10218.88
41	547.46	479.34	68.13	10218.88	9739.55
42	547.46	482.53	64.93	9739.55	9257.02
43	547.46	485.75	61.71	9257.02	8771.27
44	547.46	488.99	58.48	8771.27	8282.28
45	547.46	492.25	55.22	8282.28	7790.03
46	547.46	495.53	51.93	7790.03	7294.50
47	547.46	498.83	48.63	7294.50	6795.67
48	547.46	502.16	45.30	6795.67	6293.51
49	547.46	505.51	41.96	6293.51	5788.01
50	547.46	508.88	38.59	5788.01	5279.13
51	547.46	512.27	35.19	5279.13	4766.86
52	547.46	515.68	31.78	4766.86	4251.18
53	547.46	519.12	28.34	4251.18	3732.06
54	547.46	522.58	24.88	3732.06	3209.47
55	547.46	526.07	21.40	3209.47	2683.41
56	547.46	529.57	17.89	2683.41	2153.83
57	547.46	533.10	14.36	2153.83	1620.73
58	547.46	536.66	10.80	1620.73	1084.07
59	547.46	540.24	7.23	1084.07	543.84
60	547.46	543.84	3.63	543.84	0.00