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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
Publisher: Cengage Learning
ISBN: 9781337274203

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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

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, 4.5% mortgage for 8 years.

Explanation of Solution

Given Information:

The mortgage maturity period is 15 years that has principal amount $2,000,000 and the rate of interest is 4.5% for 8 years.

Formula used:

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

PV=PMT1(1+i)(nk)i

Calculation:

Consider the provided information, “A $2,000,000, 15 years, 4.5% mortgage for 8 years is taken.”

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

Hence, PV=2,000,000

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

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

n=15×12=180

And since, the interest rate is 4.5% mortgage per year.

Hence, i is given by:

4.5%=4.5100=0.045

Since, there are 12 periods,

Interest per period is:

i=0.04512

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

PMT=PVi1(1+i)n

Therefore, substitute 2,000,000 for PV, 180 for n and 0.04512 for i in PMT=PVi1(1+i)n.

PMT=2,000,000(0.045/121(1+0.045/12)180)

Use TI83 calculator and steps of calculator is shown below;

Step 1: Press the ON key.

Step 2: Enter the expression as 2000000*(0.045/12)/(1(1+0.045/12)^(180))

Step 3: Press enter to get the result.

The result obtained is:

2000000*(0.045/12)/(1(1+0.045/12)^(180))=15299.87

Therefore,

PMT=2,000,000(0

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