Question

When you purchased your house, you took out a 30-year annual-payment mortgage with an interest rate of 6 percent per year (compounded annually). The annual payment on the mortgage is $12,000, paid at the end of each year. You have just made a payment and have now decided to pay the mortgage off by repaying the outstanding balance. What is the payoff amount if you have lived in the house for 12 years (so there are 18 years left on the mortgage)

Answer 1

Answer: $129,931.24

Explanation:

Annuity is a stream of equal cash flows that has a specified number of periods. To get the payoff amount for living in the house for 12 years, we calculate the present value of the annuity.

The payoff amount for living in the house for 12 years is $129,931.24.

Check the attached document for the calculation.

Answer 2

Answer:

$129,931

Explanation:

we first need to determine the present value of the debt (or principal) using the annuity formula:

PV = P x {[1 - (1 + r)⁻ⁿ] / r}

• r = 6%
• P = 12,000
• n = 30

PV = 12,000 x {[1 - (1 + 6%)⁻³⁰] / 6%} = 12,000 x 13.76 = $165,178

now we must prepare an amortization schedule, we can do it on excel or by hand:

year    beginning      payment      principal      interest         ending

          principal                              paid             paid              principal

1          165,178           12,000         2,089          9,910            163,089

2         163,089          12,000         2,215           9,785           160,874

3         160,874          12,000         2,347           9,652           158,526

4         158,526          12,000         2,488           9,512            156,038

5         156,038          12,000         2,637           9,362           153,400

6         153,400          12,000         2,795           9,204           150,604

7         150,604          12,000         2,963           9,036           147,640

8         147,640          12,000         3,142            8,858            144,499

9         144,499          12,000         3,330           8,670             141,169

10        141,169           12,000         3,530           8,470             137,639

11         137,639         12,000          3,742           8,258             133,897

12        133,897         12,000          3,966          8,034            $129,931