Understanding the Mathematics of Personal Finance

# LOANS WITH FIRST PAYMENT DUE IMMEDIATELY

When you borrow cash, you don’t usually make your first payment on the loan at the time you get your cash; instead, you wait for a month (or whatever the payment period is). When you never actually see the cash, for example, if you drive away in a financed new car, sometimes the first payment on the loan is due immediately rather than a month later.[11] Some online calculators let you take this variation into account.

The third tab in my spreadsheet, labeled Loan V2, calculates amortization tables for loans where the first payment is due at the date of the start of the loan.

In Table 3.8, I show (the first few lines of) a 15-year loan taken in May of 2008 for \$175,000 at an APR of 8.00% with the first payment due immediately. As you can see, the format is the same as that of the Loan tab, so make sure you’re using the correct tab when you study a loan.

Table 3.8 A Loan With the First Payment Due When the Loan Is Taken

This sheet for loans with the first payment due at the start of the loan

 Start Month: 5 Start Year: 2008 Nr Mnthly Pmts 180 Principal \$175,000 Rate 8.00%
 Pmt Nr Mnth Year Balance (\$) Payment (\$) Interest (\$) Tot Int/Year (\$) 1 5 2008 173,338.68 1,661.32 0.00 0.00 2 6 2008 172,832.96 1,661.32 1,155.59 1,155.59 3 7 2008 172,323.86 1,661.32 1,152.22 2,307.81 4 8 2008 171,811.37 1,661.32 1,148.83 3,456.64 5 9 2008 171,295.47 1,661.32 1,145.41 4,602.05 6 10 2008 170,776.12 1,661.32 1,141.97 5,744.02 7 11 2008 170,253.31 1,661.32 1,138.51 6,882.52 8 12 2008 169,727.02 1,661.32 1,135.02 8,017.55 9 1 2009 169,197.22 1,661.32 1,131.51 1,131.51 10 2 2009 168,663.88 1,661.32 1,127.98 2,259.49

The noticeable differences between the Loan V2 sheet and the earlier Loan sheet are that the Pmt Nr column starts with 1 rather than with 0. The first payment occurs at Pmt Nr 1, and the balance is reduced from the principal immediately. What’ s happening is that the borrower is receiving \$175,000 and immediately returning \$1,661.32. In other words, this is really a \$173,338.68 loan.

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