Friday, May 10, 2019

Calculating interest payments for a period


This problem shows how to use the IPMT function to calculate interest payments for three loans for a person with good credit and for a person with poor credit.


Question One:  Consider two people one with good credit and one with bad credit.   Each person has a car loan, a 30-year FRM, and a personal student loan.   The date of origination of each loan, the term of each loan, and the interest rate on each loan for the two people are presented in the table below.  What was the interest paid on these loans for the two people in 2014?


Bad Credit Rate
Good Credit Rate
Loan Term Years
Loan Origination Date
Initial Loan Balance
Car Loan
0.11
0.04
6
1/1/13
$15,000
 Student Loan 
0.12
0.06
20
1/1/10
$45,000
Mortgage
0.055
0.0325
30
6/1/13
$320,000



Answer:   I will use the IPMT function to get the monthly loan information for each loan and each month in 2014.     The input variables for the IPMT function are 1) RATE (monthly interest rate), 2) PER (age of the loan in each month), 3) NPER (the term of the loan), and 4) PV (the loan balance.)

The monthly interest rate is simply the annual rate divided by 12.

The term of each loan and the initial loan balance for each loan is given in the chart.

The age of the loan on January 1 2014 and on subsequent dates can be obtained by counting from the loan origination date.   January 2014 is the 13th month of the car loan, the 49th month for the personal student loan, and the 7th month for the mortgage.

The three charts below give monthly and 2014 total interest payment calculations from the car loan, the personal student loan, and the mortgage for the person with bad and good credit.    

·      The person with bad credit pays a total of $22,462 in interest in 2014, ($1,342 on the car loan, $3,748 for the student loan, and $17,373 on the mortgage.)

·      The person with good credit pays a total of $12,358 in interest in 2014 ($467 on the car loan, $1,691 on the student loan, and $10,200 on the mortgage.)
Car Loan Assumptions
Bad Credit
Good Credit
Rate
0.11
0.04
Term
72
72
Loan Balance
$15,000
$15,000
Car Loan 2014
 Interest Payments
13
-$120.37
-$42.48
14
-$118.86
-$41.84
15
-$117.33
-$41.19
16
-$115.79
-$40.55
17
-$114.23
-$39.90
18
-$112.66
-$39.25
19
-$111.08
-$38.60
20
-$109.48
-$37.95
21
-$107.87
-$37.29
22
-$106.24
-$36.63
23
-$104.59
-$35.97
24
-$102.94
-$35.31
Total
-$1,341.44
-$466.95



Personal Student Loan Assumptions
Bad Credit
Good Credit
Rate
0.12
0.06
Term
120
120
Loan Balance
$45,000
$45,000
Personal Student Loan
Interest Payments 2014
49
-$330.24
-$150.73
50
-$327.08
-$148.98
51
-$323.90
-$147.23
52
-$320.68
-$145.47
53
-$317.43
-$143.70
54
-$314.15
-$141.92
55
-$310.83
-$140.13
56
-$307.49
-$138.33
57
-$304.11
-$136.52
58
-$300.69
-$134.71
59
-$297.24
-$132.88
60
-$293.76
-$131.05
Total
-$3,747.59
-$1,691.64




Mortgage Rate Assumptions
Bad Credit
Good Credit
Rate
0.055
0.0325
Term
360
360
Loan Balance
$320,000
$320,000
Mortgage Interest
Payments in 2014
7
-$1,456.92
-$858.06
8
-$1,455.27
-$856.61
9
-$1,453.62
-$855.16
10
-$1,451.95
-$853.71
11
-$1,450.28
-$852.25
12
-$1,448.60
-$850.78
13
-$1,446.91
-$849.31
14
-$1,445.21
-$847.84
15
-$1,443.51
-$846.37
16
-$1,441.80
-$844.89
17
-$1,440.08
-$843.40
18
-$1,438.35
-$841.92
Total
-$17,372.50
-$10,200.31


Note that this problem could be also solved with the CUMIPMT function.



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