Understanding the Mathematics of Personal Finance

IRREGULAR PAYMENTS

I f you decide to make a payment that is larger than your regular payment, your balance will be reduced by an extra amount. Your lender should reduce your balance, and hence the accrued interest until your loan is paid off, accordingly. Similarly, if you make a payment that is smaller than your regular payment, some corrections must be made. In this latter case, penalties might be added to the balance as well as corrections to the calculations.

Different lenders handle these situations differently. This makes it impossible for me to discuss or present a spreadsheet that will handle the general case. Instead, I ’ ll just show a couple of possibilities here. What I ’ m doing is mathematically correct, but remember that it might not apply directly to your loan.

l ’ ll use the same loan as shown in Table 3.7 і Suppose that in May 2006, I received a good income tax refund and I want to apply my newfound extra money to my loan. For payment number 10, I’ll pay $10,000 instead of my regular $3,134.17.

Table 3.9 The Amortization Spreadsheet with Extra Payments Inserted

Pmt Nr

Mnth

Year

Balance ($)

Payment ($)

Interest ($)

Tot Int/Year ($)

0

7

2005

350,000.00

0.00

0.00

0.00

1

8

2005

348,890.00

3,134.17

2,024.17

2,024.17

2

9

2005

347,773.57

3,134.17

2,017.75

4,041.91

3

10

2005

346,650.69

3,134.17

2,011.29

6,053.20

4

11

2005

345,521.32

3,134.17

2,004.80

8,058.00

5

12

2005

344,385.42

3,134.17

1,998.26

10,056.27

6

1

2006

343,242.94

3,134.17

1,991.70

1,991.70

7

2

2006

342,093.86

3,134.17

1,985.09

3,976.78

8

3

2006

340,938.13

3,134.17

1,978.44

5,955.23

9

4

2006

339,775.72

3,134.17

1,971.76

7,926.99

10

5

2006

331,740.76

10,000.00

1,965.04

9,892.02

11

6

2006

330,588.71

3,070.62

1,918.57

11,810.59

12

7

2006

329,429.99

3,070.62

1,911.90

13,722.49

13

8

2006

328,264.57

3,070.62

1,905.20

15,627.70

14

9

2006

327,092.42

3,070.62

1,898.46

17,526.16

15

10

2006

326,984.10

2,000.00

1,891.68

19,417.85

16

11

2006

325,794.45

3,080.71

1,891.06

21,308.90

17

12

2006

324,597.93

3,080.71

1,884.18

23,193.08

18

1

2007

323,394.48

3,080.71

1,877.26

1,877.26

19

2

2007

322,184.07

3,080.71

1,870.30

3,747.56

20

3

2007

320,966.66

3,080.71

1,863.30

5,610.85

On my spreadsheet, just type $10,000 in for the correct payment as shown in Table 3.9. (If you haven’t done it already, please take a minute and read the informa­tion in Chapter 15 on how to reestablish the original spreadsheet calculations after you’ve changed them.) As you can see, the payments after the $10,000 payment reflect the change and correctly show the new regular payment necessary to exactly pay off the loan at the end of 180 months. The balance, interest, and total interest per year columns are also correct.

Just to show what can be done, I changed payment 15 to a payment of $2,000.00. Again, the spreadsheet automatically corrected all of its calculations to reflect this change.

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