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Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

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BuyFindarrow_forward

Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447
Textbook Problem

Marc Bove purchased a home with a $78,500 mortgage at 9 % for 15 years. Calculate the monthly payment and prepare an amortization schedule for the first four months of Marc’s loan.

Payment Number MonthlyPayment MonthlyInterest Portion Used to Reduce Principal Loan Balance
01 $78,500.00
2
3
4

To determine

To calculate: The monthly payment and formulate an amortization schedule for the first four months of marc’s loan if he purchased a home with a $78,500 mortgage at 9% for 15 years.

Explanation

Given Information:

The mortgage is $78,500, the rate is 9% and time is 15 years.

Formula used:

To calculate the monthly mortgage payment by using an Amortization table and also to calculate total interest formula, use the following steps.

Step 1: Find the number of $1,000s financed.

Number of $1,000 financed=Amount financed1,000

Step 2: With the help of the amortization table, calculate the table factor.

Step 3: Calculate the monthly payment using the table factor:

Monthly payment=Number of $1,000 financed×Table factor

Step 4: Calculate the total interest of the loan.

Total interest=(Monthly payment×number of payments) Amount financed

The procedure, to create an amortization schedule for a loan is given below:

Step 1: With the help of the amortization table, calculate the amount of monthly payment.

Step 2: Find the amount of interest for the current month using relation I=PRT, Where P is the current outstanding balance of the loan, R is the annual interest rate and T is 112.

Step 3: Calculate the portion of the payment used to reduce principle.

Portion of payment reducing principle =Monthly payment Interest

Step 4: Find the outstanding balance of the mortgage loan.

Outstanding balance =Previous balancePortion of payment reducing principle 

Step 5: Repeat steps 2, 3 and 4 for each succeeding month and enters the values on a schedule with respective labels.

Calculation:

Firstly, find the monthly payment.

Step 1: Find the number of $1,000s financed.

Number of $1,000 financed=Amount financed1,000=$78,5001,000=78.5

Step 2: Calculate the table factor.

Table factor for 9%, 15 years is 10.15.

Step 3: Calculate the monthly payment using the table factor:

Monthly payment=Number of $1,000 financed×Table factor=78.5×10.15=796.775$796.78

Now, follow the steps to create an amortization schedule for a loan:

Monthly payment is $796.78.

For month 1:

Interest=Principle×Rate×Time=78,500×.09×112=$588.75

Now, calculate the portion of the payment used to reduce principle.

Portion of payment reducing principle =Monthly payment Interest=796.78588.75=$208.03

Find the outstanding balance of the mortgage loan.

Outstanding balance =Previous balancePortion of payment reducing principle =$78,500208.03=$78,291.97

Repeat steps 2, 3 and 4 for four months:

For month 2, do the same calculation as done for month 1.

Month 2:

Interest=Principle×Rate×Time=78,291.97×.09×112=$587.19

Calculate the portion of the payment used to reduce principle.

Portion of payment reducing principle =Monthly payment Interest=796.78587.19=$209.59

Find the outstanding balance of the mortgage loan.

Outstanding balance =Previous balancePortion of payment reducing principle =78,291.97209.59=$78,082

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