ðɪs dˌɛɹɪvˈeɪʃən ˈɪləstɹˌeɪts θɹˈiː kˈiː kəmpˈoʊnənts ʌv fˈɪkstɹˈeɪt lˈoʊnz: wˈʌn ðə fˈɪkst mˈʌnθli pˈeɪmənt dᵻpˈɛndz əpˌɑːn ðɪ ɐmˈaʊnt bˈɑːɹoʊd, ðɪ ˈɪntɹɛst ɹˈeɪt, ænd ðə lˈɛŋθ ʌv tˈaɪm ˌoʊvɚ wˌɪtʃ ðə lˈoʊn ɪz ɹᵻpˈeɪd; tˈuː ðɪ ɐmˈaʊnt ˈoʊd ˈɛvɹi mˈʌnθ ˈiːkwəlz ðɪ ɐmˈaʊnt ˈoʊd fɹʌmðə pɹˈiːviəs mˈʌnθ plˈʌs ˈɪntɹɛst ˌɔn ðæt ɐmˈaʊnt, mˈaɪnəs ðə fˈɪkst mˈʌnθli pˈeɪmənt; θɹˈiː ðə fˈɪkst mˈʌnθli pˈeɪmənt ɪz tʃˈoʊzən sˌoʊ ðætðə lˈoʊn ɪz pˈeɪd ˈɔf ɪn fˈʊl wɪð ˈɪntɹɛst æt ðɪ ˈɛnd ʌv ɪts tˈɜːm ænd nˈoʊmˌoːɹ mˈʌni ɪz ˈoʊd.
This derivation illustrates three key components of fixed-rate loans: (1) the fixed monthly payment depends upon the amount borrowed, the interest rate, and the length of time over which the loan is repaid; (2) the amount owed every month equals the amount owed from the previous month plus interest on that amount, minus the fixed monthly payment; (3) the fixed monthly payment is chosen so that the loan is paid off in full with interest at the end of its term and no more money is owed.