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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 3.3, Problem 36E

Textbook Problem

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In Exercises 33–38, determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) [**hinT:** See Example 7.]

A $2,000,000, 15-year, 4.5% mortgage after 8 years

To determine

**To calculate:** The outstanding principal of a $2,000,000, 15 years,

**Given Information:**

The mortgage maturity period is 15 years that has principal amount $2,000,000 and the rate of interest is

**Formula used:**

Consider after *k* months there are *PMT* remaining to make. The outstanding payment is the present value necessary to fund these payments. Hence, the outstanding principal is given by:

**Calculation:**

Consider the provided information, “A $2,000,000, 15 years,

Since, the starting balance of the account is $2,000,000,

Hence,

Also, since they have to be accumulated for a period of 15 years,

In order to convert it into months, multiply by 12.

And since, the interest rate is

Hence, *i* is given by:

Since, there are 12 periods,

Interest per period is:

Since, the amount that must be paid into the account at the end of each period is given by:

Therefore, substitute 2,000,000 for *PV*, 180 for *n* and *i* in

Use TI83 calculator and steps of calculator is shown below;

Step 1: Press the ON key.

Step 2: Enter the expression as

Step 3: Press enter to get the result.

The result obtained is:

Therefore,

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