(a)
Graphical representation of monthly payment as a function of interest rate.
Answer to Problem 106P
Graphical representation of monthly payment as a function of interest rate.
Explanation of Solution
Given information:
- Loan Amount - $900
- Time period − 1 years
- Rate of Interest − 4-14% 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:
Calculation:
The loan amount is $900. 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.
Based on the above information, the following table can be created:
Time Period (in years) | Time Period (in months) | Rate of Interest (compounded annually) | Rate of Interest (compounded monthly) | Loan Amount to be paid | Per month repayment |
1 | 12 | 4% | 0.003 | 900 | 76.63 |
1 | 12 | 5% | 0.004 | 900 | 77.05 |
1 | 12 | 6% | 0.005 | 900 | 77.46 |
1 | 12 | 7% | 0.006 | 900 | 77.87 |
1 | 12 | 8% | 0.007 | 900 | 78.29 |
1 | 12 | 9% | 0.008 | 900 | 78.71 |
1 | 12 | 10% | 0.008 | 900 | 79.12 |
1 | 12 | 11% | 0.009 | 900 | 79.54 |
1 | 12 | 12% | 0.010 | 900 | 79.96 |
1 | 12 | 13% | 0.011 | 900 | 80.39 |
1 | 12 | 14% | 0.012 | 900 | 80.81 |
Now, the graph will be plotted between the rate of interest compounded annually and per month repayment. The graph will look as:
(b)
Graphical representation of monthly payment as a function of time period.
Answer to Problem 106P
Graphical representation of monthly payment as a function of interest rate.
Explanation of Solution
Given information:
- Loan Amount - $900
- Rate of Interest − 6% per annum.
- Time period − 36-84 months
- 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:
Calculation:
The loan amount is $900. 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.
Based on this information, following table can be created:
Time Period (in months) | Rate of Interest (compounded annually) | Rate of Interest (compounded monthly) | Loan Amount to be paid | Per month repayment |
36 | 6% | 0.005 | 900 | 27.38 |
37 | 6% | 0.005 | 900 | 26.70 |
38 | 6% | 0.005 | 900 | 26.06 |
39 | 6% | 0.005 | 900 | 25.46 |
40 | 6% | 0.005 | 900 | 24.88 |
41 | 6% | 0.005 | 900 | 24.33 |
42 | 6% | 0.005 | 900 | 23.81 |
43 | 6% | 0.005 | 900 | 23.31 |
44 | 6% | 0.005 | 900 | 22.84 |
45 | 6% | 0.005 | 900 | 22.38 |
46 | 6% | 0.005 | 900 | 21.95 |
47 | 6% | 0.005 | 900 | 21.53 |
48 | 6% | 0.005 | 900 | 21.14 |
49 | 6% | 0.005 | 900 | 20.75 |
50 | 6% | 0.005 | 900 | 20.39 |
51 | 6% | 0.005 | 900 | 20.04 |
52 | 6% | 0.005 | 900 | 19.70 |
53 | 6% | 0.005 | 900 | 19.37 |
54 | 6% | 0.005 | 900 | 19.06 |
55 | 6% | 0.005 | 900 | 18.76 |
56 | 6% | 0.005 | 900 | 18.47 |
57 | 6% | 0.005 | 900 | 18.19 |
58 | 6% | 0.005 | 900 | 17.91 |
59 | 6% | 0.005 | 900 | 17.65 |
60 | 6% | 0.005 | 900 | 17.40 |
61 | 6% | 0.005 | 900 | 17.15 |
62 | 6% | 0.005 | 900 | 16.92 |
63 | 6% | 0.005 | 900 | 16.69 |
64 | 6% | 0.005 | 900 | 16.47 |
65 | 6% | 0.005 | 900 | 16.25 |
66 | 6% | 0.005 | 900 | 16.04 |
67 | 6% | 0.005 | 900 | 15.84 |
68 | 6% | 0.005 | 900 | 15.65 |
69 | 6% | 0.005 | 900 | 15.45 |
70 | 6% | 0.005 | 900 | 15.27 |
71 | 6% | 0.005 | 900 | 15.09 |
72 | 6% | 0.005 | 900 | 14.92 |
73 | 6% | 0.005 | 900 | 14.75 |
74 | 6% | 0.005 | 900 | 14.58 |
75 | 6% | 0.005 | 900 | 14.42 |
76 | 6% | 0.005 | 900 | 14.26 |
77 | 6% | 0.005 | 900 | 14.11 |
78 | 6% | 0.005 | 900 | 13.96 |
79 | 6% | 0.005 | 900 | 13.82 |
80 | 6% | 0.005 | 900 | 13.68 |
81 | 6% | 0.005 | 900 | 13.54 |
82 | 6% | 0.005 | 900 | 13.41 |
83 | 6% | 0.005 | 900 | 13.28 |
84 | 6% | 0.005 | 900 | 13.15 |
Now, the graph will be plotted between the time period and per month repayment. The graph will look as:
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Chapter 4 Solutions
ENGR.ECONOMIC ANALYSIS
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