ðə pˌɑːlɪnˈoʊmɪəl ɐpˈɪɹɪŋ bᵻfˌoːɹ ðə fˈɪkst mˈʌnθli pˈeɪmənt sˈiː wɪð ɪz ɐ dʒˌiːoʊmˈɛtɹɪk sˈɪɹiz, wˌɪtʃ hɐz ɐ sˈɪmpəl klˈoʊzdfˈɔːɹm ɛkspɹˈɛʃən əbtˈeɪnd fɹʌm əbzˈɜːvɪŋ ðæt bɪkˈʌz ˈɔːl bˌʌt ðə fˈɜːst ænd lˈæst tˈɜːmz ɪn ðɪs dˈɪfɹəns kˈænsəl ˈiːtʃ ˈʌðɚɹ ˈaʊt.
The polynomial  appearing before the fixed monthly payment c (with ) is a geometric series, which has a simple closed-form expression obtained from observing that  because all but the first and last terms in this difference cancel each other out.