Recall the ongoing example from Sections 4.4 and 4.5 about Pat and Tracy's 30-year mortgage. For instance, see Example 4.5.3. How much will they owe on their mortgage when 253 payments remain? Example 4.5.3 Assuming that they make all their payments as scheduled, how much will Pat and Tracy owe on their mortgage after 5 years? 10 years? 15 years? 20 years? 25 years? Following the approach used above, we find after 5 years they will have made 60 payments. And so 360 - 60 = 300 payments remain. The amount they owe is the present value of those payments. So: PV = PMT anji PV = $1,072.49 d30010.072/12 PV = $1,072.49(138.96827618) PV = $149,042.09 The remaining calculations are essentially the same. The results are displayed in the table below Elapsed Remaining Annuity Years Payments Factor Remaining Balance 5 300 138.96827618 $149,042.09 10 240 127.00843213 $136,215.27 15 180 109.88446602 $117,849.99 20 120 85.36656977 $91,554.79 25 60 50.26213003 $53,905.63