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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Monthly Payments You are taking out a home mortgage for $200,000. and you are given the options below. Find the monthly payment and the total amount of money you will pay for each mortgage. Which option would you choose? Explain your reasoning.

(a) A fixed annual rate of 5 % , over a term of 30 years.

(b) A fixed annual rate of 6 % , over a term of 20 years.

(c) A fixed annual rate of 6.5 % , over a term of 15 years.

(a)

To determine

To calculate: The monthly payment and the total amount of money that would be paid for each mortgage when a home mortgage for $200,000 has been taken out at a fixed annual rate of 5% over a term of 30 years.

Explanation

Given Information:

A home mortgage for $200,000 has been taken out at a fixed annual rate of 5% over a term of 30 years.

Formula used:

The formula used to calculate monthly installment M is given by,

M=(Pr12)1[11+(r/12)]12t

Where P is the amount, r is the rate and t is the time period.

Calculation:

The amount taken for mortgage is $200,000 at the annual rate of 5% over a term of 30 years.

Thus, P=200,000, r=0.05 and t=30.

Now substitute all the values in the formula M=(Pr12)1[11+(r/12)]12t as,

M=(Pr12

(b)

To determine

To calculate: The monthly payment and the total amount of money that would be paid for each mortgage when a home mortgage for $200,000 has been taken out at a fixed annual rate of 6% over a term of 20 years.

(c)

To determine

To calculate: The monthly payment and the total amount of money that would be paid for each mortgage when a home mortgage for $200,000 has been taken out at a fixed annual rate of 6.5% over a term of 15 years.

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