Understanding the Mathematics of Personal Finance

# ONLINE CALCULATORS

These calculators are so numerous that I’m sure you can find many more in addition to the ones listed below. These look fairly good and are easy to use without first having to register or “get a quote.” You’ll also see some unusual numbers such as “average monthly interest.” Please don’t take these too seriously—read about Present Value in Chapter 7 . Most of these sites will present a full amortization table if requested. This can be very convenient:

4.1 FIXED RATE MORTGAGES

Mortgage loan interest rates can be arranged in any of several ways. First, there is the fixed interest loan. This is what I have presented in the last chapter. The interest rate stays the same for the entire repayment period. Typically, you commit to pay the loan back in a fixed period such as monthly payments for 15 years and fixed payments are calculated. In most cases, you can make extra payments (or increase the amount of some of your payments). This, of course, reduces your outstanding balance and therefore reduces the interest charged. I’ll go through some examples of these variations below. In some cases, you’re allowed to pay just the interest, in which case the balance stays the same. Most mortgages do not come with prepay­ment penalties. This means that there is no charge for paying off or reducing the

Table 4.1 Fixed Rate, Fixed Payment Mortgage Amortization Table

 Pmt Nr Month Year Balance (\$) Payment (\$) Interest (\$) Tot Int/Year (\$) 0 7 2009 200,000.00 0.00 0.00 0.00 1 8 2009 199,567.14 1,432.86 1,000.00 1,000.00 2 9 2009 199,132.11 1,432.86 997.84 1,997.84 3 10 2009 198,694.91 1,432.86 995.66 2,993.50 4 11 2009 198,255.52 1,432.86 993.47 3,986.97 5 12 2009 197,813.94 1,432.86 991.28 4,978.25 6 1 2010 197,370.15 1,432.86 989.07 989.07 7 2 2010 196,924.13 1,432.86 986.85 1,975.92 8 3 2010 196,475.89 1,432.86 984.62 2,960.54 9 4 2010 196,025.41 1,432.86 982.38 3,942.92 238 5 2029 2,844.37 1,432.86 21.28 176.28 239 6 2029 1,425.73 1,432.86 14.22 190.50 240 7 2029 0.00 1,432.86 7.13 197.63

balance on the loan sooner than the original schedule prescribes. Don’t assume too much here—this is an important point and you should read your mortgage loan contract very carefully before you sign it.

For analyzing a basic fixed interest, fixed payment loan, the website references given in Chapter 3 will do the job. If you’re going to vary the payments, a simple calculator can’t adequately do the job; a spreadsheet is definitely the way to go. I’ l l start with a simple spreadsheet and fixed payments just so that I can review how things are set up. Then, I’ll show how to modify this to accept any payments whatsoever and to update all information and predictions. The spreadsheet Ch4Mortgages. xls on my website handles all of the calculations in this chapter.

The first tab on my spreadsheet, Basic, is identical to the Loan tab on the Chapter 3 spreadsheet. The use is the same, and the examples are the same. The only differ­ence is that now we call the loan a mortgage loan.

As an example, consider a \$200,000 principal and a 20tyear (240 monthly payment) mortgage loan at 6.00% annual percentage rate (APR). Table 4.1 shows the spreadsheet results. I did not include the input region (to the left of the green line) because this is identical to the examples in the previous chapter. The loan is taken on a day in July 2009.

Looking at Table 4.1, or the spreadsheet, the regular monthly payment is \$1,432.86.

If your loan agreement allows it, you might decide to just make interest pay­ments or a reduced amount payment for some number of months. Assume that at payment number 15, in October 2010, you want to make interest-only payments for a few months. The interest accrued in the month coming up to payment number 15 is \$968.69. If you change the payment amount at this time to just this amount, you’ll see that the interest for payment 16 changes to this same amount. This

Table 4.2 Repeat of Table 4.1 with Interest-Only and a Single Large Payment Inserted

 Pmt Nr Month Year Balance (\$) Payment (\$) Interest (\$) Tot Int/Year(\$) 12 7 2010 194,660.40 1,432.86 975.59 6,876.50 13 8 2010 194,200.84 1,432.86 973.30 7,849.80 14 9 2010 193,738.98 1,432.86 971.00 8,820.81 15 10 2010 193,738.99 968.69 968.69 9,789.50 16 11 2010 193,738.99 968.69 968.69 10,758.20 17 12 2010 193,739.00 968.69 968.69 11,726.89 18 1 2011 193,739.00 968.69 968.69 968.69 19 2 2011 193,739.01 968.69 968.70 1,937.39 20 3 2011 193,739.01 968.69 968.70 2,906.09 21 4 2011 193,253.68 1,454.03 968.70 3,874.78 22 5 2011 192,765.92 1,454.03 966.27 4,841.05 23 6 2011 192,275.73 1,454.03 963.83 5,804.88 24 7 2011 191,783.08 1,454.03 961.38 6,766.26 25 8 2011 187,741.99 5,000.00 958.92 7,725.17 26 9 2011 187,253.63 1,427.07 938.71 8,663.88 27 10 2011 186,762.82 1,427.07 936.27 9,600.15 28 11 2011 186,269.57 1,427.07 933.81 10,533.96 29 12 2011 185,773.84 1,427.07 931.35 11,465.31

is correct—since you haven’t changed the balance at payment 15, the interest accrued the following month should be the same as the interest accrued the previous month.

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.

In Table 4.2, you’ll see the same loan as shown in Table 4.1 but with interest- only payments being made for 6 months. At payment number 21, the regular monthly payment has jumped from \$1,432.86 to \$1,454.03 to pay off the loan at the end of 240 months (from the date of taking the loan).

Also shown in Table 4.2 is the result of making a \$5,000 payment at payment number 25. After this payment, the regular monthly payment drops to \$1,427.07.

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