Question

Your family purchased a house three years ago. When you bought the house you financed it with a $185,000 mortgage with an 8.2 percent nominal interest rate, with monthly payments. The mortgage was for 15 yearsWhat is the remaining balance on your mortgage today?

What the PV of an ordinary annuity with 10 payments of \$66,450 If the appropriate Interest rate is 74 percent?

Answer 1

1). Loan Balance after t payments = [Loan Amount * {(1 + r)^n - (1 + r)^t}] / [(1 + r)^n - 1]

Loan Balance after 36 payments(i.e. today) = [$185,000 * {(1 + 0.082/12)^(15*12) - (1 + 0.082/12)^36}] / [(1 + 0.082/12)^(15*12) - 1]

= [$185,000 * {3.4069 - 1.2778}] / [3.4069 - 1]

= [$185,000 * 2.1291] / 2.4069

= $393,886.63 / 2.4069

= $163,645.75

2). PV of Annuity = Annual Payment * [{1 - (1 + r)^-n} / r]

= $66,450 * [{1 - (1 + 0.74)^-10} / 0.74]

= $66,450 * [0.9961 / 0.74]

= $66,450 * 1.3460

= $89,444.30