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The Economic Consequences of Homelessness in The US

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= -PMT(6.5 / 100 / 12, 30 * 12, 200000)<br />

= ((6.5 / 100 / 12) * 200000) / (1 - ((1 + (6.5 / 100 / 12)) ^ (-30 * 12)))<br />

= 1264.14<br />

<strong>The</strong> follow<strong>in</strong>g derivation <strong>of</strong> this formula illustrates how fixed-rate mortgage loans work.<br />

<strong>The</strong> amount owed on the loan at the end <strong>of</strong> every month equals the amount owed from<br />

the previous month, plus the <strong>in</strong>terest on this amount, m<strong>in</strong>us the fixed amount paid every<br />

month. This fact results <strong>in</strong> the debt schedule:<br />

Amount owed at <strong>in</strong>itiation:<br />

Amount owed after 1 month:<br />

Amount owed after 2 months:<br />

Amount owed after 3 months:<br />

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .<br />

Amount owed after N months:<br />

<strong>The</strong> polynomial<br />

appear<strong>in</strong>g before the fixed<br />

monthly payment c (with<br />

) is called a cyclotomic polynomial; it has a simple<br />

closed-form expression obta<strong>in</strong>ed from observ<strong>in</strong>g that<br />

Page 211 <strong>of</strong> 289

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