Homework #2 Solution

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Description

Description:

You have just purchased a stereo system that cost $1000 on the following credit plan: no down payment, an interest rate of 18% per year (and hence 1.5% per month), and monthly payments of $50. The monthly payment of $50 is used to pay the interest, and whatever is left is used to pay part of the remaining debt. Hence, the first month you pay 1.5% of $1000 in interest. That is $15 in interest. The remaining $35 is deducted from your debt, which leaves you with a debt of $965.00. The next month you pay interest of 1.5% of $965.00, which is $14.48. Hence, you can deduct $35.52 (which is $50–$14.48) from the amount you owe.

Write a program that will tell you how many months it will take you to pay off this loan in particular and any loan in general. Your program also needs to calculate the total amount of interest paid over the life of any loan. Use a loop to calculate the amount of interest and the size of the debt after each month. Your program must output the monthly amount of interest paid and remaining debt. Use a variable to count the number of loop iterations and hence the number of months until the debt is zero. You may want to use other variables as well. The last payment may be less than $50 if the debt is small, but do not forget the interest. If you owe $50, then your monthly payment of $50 will not pay off your debt, although it will come close. One month’s interest on $50 is only 75 cents.

Here is a sample dialog (where the user input is depicted as Bold, but you do not need to display user input in bold.):

Loan Amount: 1000

Interest Rate (% per year): 18

Monthly Payments: 50

1

******************************************************

Amortization Table

******************************************************

Month

Balance Payment Rate

Interest Principal

0

$1000.00 N/A

N/A

N/A

N/A

1

$965.00

$50.00

1.5

$15.00

$35.00

2

$929.48

$50.00

1.5

$14.48

$35.53

3

$893.42

$50.00

1.5

$13.94

$36.06

4

$856.82

$50.00

1.5

$13.40

$36.60

5

$819.67

$50.00

1.5

$12.85

$37.15

6

$781.97

$50.00

1.5

$12.30

$37.70

7

$743.70

$50.00

1.5

$11.73

$38.27

8

$704.85

$50.00

1.5

$11.16

$38.84

9

$665.42

$50.00

1.5

$10.57

$39.43

10

$625.40

$50.00

1.5

$9.98

$40.02

11

$584.79

$50.00

1.5

$9.38

$40.62

12

$543.56

$50.00

1.5

$8.77

$41.23

13

$501.71

$50.00

1.5

$8.15

$41.85

14

$459.24

$50.00

1.5

$7.53

$42.47

15

$416.13

$50.00

1.5

$6.89

$43.11

16

$372.37

$50.00

1.5

$6.24

$43.76

17

$327.95

$50.00

1.5

$5.59

$44.41

18

$282.87

$50.00

1.5

$4.92

$45.08

19

$237.11

$50.00

1.5

$4.24

$45.76

20

$190.67

$50.00

1.5

$3.56

$46.44

21

$143.53

$50.00

1.5

$2.86

$47.14

22

$95.68

$50.00

1.5

$2.15

$47.85

23

$47.12

$50.00

1.5

$1.44

$48.56

24

$0.00

$47.83

1.5

$0.71

$47.12

******************************************************

It takes 24 months to pay off the loan.

Total interest paid is: $197.83

Your program’s output should LITERALLY EXACTLY match the style of the sample output, you do not need to line up the columns, but I do need spaces in between. Do not miss the dollar sign.

In what follows, you find a second case used to test the correctness of your program.

Loan Amount: 2000

Interest Rate (% per year): 12

Monthly Payments: 80

2

******************************************************

Amortization Table

******************************************************

Month

Balance

Payment Rate

Interest Principal

0

$2,000.00

N/A

N/A

N/A

N/A

1

$1,940.00

$80.00

1

$20.00

$60.00

2

$1,879.40

$80.00

1

$19.40

$60.60

3

$1,818.19

$80.00

1

$18.79

$61.21

4

$1,756.38

$80.00

1

$18.18

$61.82

5

$1,693.94

$80.00

1

$17.56

$62.44

6

$1,630.88

$80.00

1

$16.94

$63.06

7

$1,567.19

$80.00

1

$16.31

$63.69

8

$1,502.86

$80.00

1

$15.67

$64.33

9

$1,437.89

$80.00

1

$15.03

$64.97

10

$1,372.27

$80.00

1

$14.38

$65.62

11

$1,305.99

$80.00

1

$13.72

$66.28

12

$1,239.05

$80.00

1

$13.06

$66.94

13

$1,171.44

$80.00

1

$12.39

$67.61

14

$1,103.15

$80.00

1

$11.71

$68.29

15

$1,034.19

$80.00

1

$11.03

$68.97

16

$964.53

$80.00

1

$10.34

$69.66

17

$894.17

$80.00

1

$9.65

$70.35

18

$823.12

$80.00

1

$8.94

$71.06

19

$751.35

$80.00

1

$8.23

$71.77

20

$678.86

$80.00

1

$7.51

$72.49

21

$605.65

$80.00

1

$6.79

$73.21

22

$531.70

$80.00

1

$6.06

$73.94

23

$457.02

$80.00

1

$5.32

$74.68

24

$381.59

$80.00

1

$4.57

$75.43

25

$305.41

$80.00

1

$3.82

$76.18

26

$228.46

$80.00

1

$3.05

$76.95

27

$150.75

$80.00

1

$2.28

$77.72

28

$72.25

$80.00

1

$1.51

$78.49

29

$0.00

$72.98

1

$0.72

$72.25

******************************************************

It takes 29 months to pay off the loan.

Total interest paid is: $312.98

Special Cases:

  1. Please think about how to deal with the last payment, which is smaller than regular payment. For example, in the above table, the regular payments are $80.00 whereas the last payment is only 72.98.

  1. Your program needs to ensure that regular payments are larger than any monthly interest. For example, in the above amortization table, your program must test if the regular monthly payment (i.e., $80.00) is larger than the monthly interest (e.g., $20.00 in the first month).

  1. If you do not address the above issue, your program may not terminate in some special cases. See the example below:

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Loan Amount: 2000

Interest Rate (% per year): 49.2

Monthly Payments: 80

******************************************************

Amortization Table

******************************************************

Month

Balance

Payment Rate

Interest Principal

0

$2,000.00

N/A

N/A

N/A

1

$2,002.00

$80.00

4.1

$82.00

-$2.00

2

$2,004.08

$80.00

4.1

$82.08

-$2.08

3

$2,006.25

$80.00

4.1

$82.17

-$2.17

4

$2,008.51

$80.00

4.1

$82.26

-$2.26

5

$2,010.85

$80.00

4.1

$82.35

-$2.35

6

$2,013.30

$80.00

4.1

$82.45

-$2.45

7

$2,015.84

$80.00

4.1

$82.55

-$2.55

8

$2,018.49

$80.00

4.1

$82.65

-$2.65

9

$2,021.25

$80.00

4.1

$82.76

-$2.76

10

$2,024.12

$80.00

4.1

$82.87

-$2.87

11

$2,027.11

$80.00

4.1

$82.99

-$2.99

12

$2,030.22

$80.00

4.1

$83.11

-$3.11

13

$2,033.46

$80.00

4.1

$83.24

-$3.24

14

$2,036.84

$80.00

4.1

$83.37

-$3.37

15

$2,040.35

$80.00

4.1

$83.51

-$3.51

16

$2,044.00

$80.00

4.1

$83.65

-$3.65

17

$2,047.80

$80.00

4.1

$83.80

-$3.80

18

$2,051.76

$80.00

4.1

$83.96

-$3.96

19

$2,055.89

$80.00

4.1

$84.12

-$4.12

Programming Environment:

Write a short program in C++. Compile and run it with g++ (-std=c++11 is recommended) compiler on the tux machine, I.e., the AU server.

It is absolutely your responsibility to ensure you code compiles and runs as intended on AU servers.

It is fine to use any IDE but please double check your program on a school machine.

Requirements:

  1. (5 points) Use comments to provide a heading at the top of your code containing your name, Auburn UserID, filename, and how to compile your code. Also describe any help or sources that you used (as per the syllabus).

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  1. (5 points) Your source code file should be named as “hw2_username.cpp”.

(replace username with your Auburn username).

  1. (40 points) No compilation error and no warning messages

  2. (10 points) Usability of your program (e.g., input and output)

  1. (40 points) Quality of your source code.

You will lose points if you: do not use the specific program file name, or do not have a comment block on EVERY program you hand in. You will lose at least 40 points if there are compilation errors or warning messages when we compile your source code.

Deliverables:

  • Submit your cpp file on Canvas. The cpp file should be named as

hw2_username.cpp” where the username is your Auburn user ID , I.e. hw2_zzz0092.cpp

  • Do NOT submit anything else!

  • Do NOT submit zipped file. Submit your cpp file directly.

Late Submission Penalty:

  • Late submissions will not be accepted and will result in a ZERO without valid excuses, in which case you should talk to Dr. Li to explain your situation.

  • GTA/Instructor will NOT accept any late submission caused by Internet latency

Rebuttal period:

  • You will be given a period of 3 days to read and respond to the comments and grades of your homework or project assignment. The TA may use this opportunity to address any concern and question you have. The TA also may ask for additional information from you regarding your homework or project.

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