The formula for finding the number of periodic payments for a loan, N, is also easily found.
Let P be the amount owed as before, Pmt be the periodic payment, and i be the decimal interest per period. If there are ppy paymemnts per year and the annualized interest rate is in percent, then it is divided by 100 and by ppy. Starting from the standard formula previously derived:
| Pmt | = |
P i ----- 1-(1+i)-N |
|
i P --- Pmt | = 1 - ( 1 + i )- N |
| ( 1 + i )- N | = | 1 | - |
i P --- Pmt |
If x = by then by definition Logbx = y. Associating b with ( 1 + i ), y with -n, and x with
| 1 | - |
i P --- Pmt |
| N = | - Log ( i + 1 ) ( 1 - |
i P --- Pmt |
) | where i is the decimal annualized interest rate divided by the payments per year |
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