Chapter 14, Problem 3AT

Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

Chapter
Section

Contemporary Mathematics for Busin...

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

Suzanne Arthurs purchased a home with a $146,100 mortgage at 6.5% for 30 years. Calculate the monthly payment and prepare an amortization schedule for the first three months of Suzanne’s loan. Payment Number Monthly Payment Monthly Interest Portion Used to Reduce Principal Loan Balance 0$146,100.00 1 _______ _______ _______ _______ 2 _______ _______ _______ _______ 3 _______ _______ _______ _______

To determine

To calculate: The monthly payment and prepare amortization schedule for the first 3 months when the principal amount is $146,100 rate of interest is 6.5 % and the term of the loan is 30 years. Explanation Given Information: Principal Amount is$ 146,100, Interest Rate is 6.5 %, Term of loan is 30 years.

Formula used:

The formula for the number of $1000 is Number of$1000s financed×Principal Amount1000

Use the table 14.1 to calculate table factor. Locate the table factor on the intersection of the number of years column and the interest rate row.

The formula for Monthly payment is

Monthly Payment=Number of 1000s financed×Table Factor

And

Interest=P×R×112

Where, P is principal amount and R is rate of interest.

Portion of payment reducing principal is given by,

Portion of payment reducing principal=Monthly paymentInterest

Outstanding balance is given by

Oustanding Balance=Previous balancePortion of payment reducing principal

Calculation:

Consider the provided values,

Principal Amount=$146,100Interest Rate=6.5%Term of Loan=30 years For first month, Calculate number of$ 1000 financed, by using the formula Number of $1000s financed×Principal Amount1000: Number of$1000s financed=Principal Amount1000=1461001000=146.1

Use the table 14.1 for locating the table factor at the intersection of 30 years (column) and 6.5 % interest rate (row)

So, the table factor for 30 years and 6.5 % rate of interest is 6.33.

To calculate Monthly Payment by using the formula Monthly Payment=Number of 1000s financed×Table Factor:

Monthly Payment=Number of 1000s financed × Table Factor=146.1×6.33=$924.81 As, Interest=P×R×112 Thus, interest becomes: Interest = P×R×112=146100×0.065×112 =$791.37

Then,

Portion of payment reducing principal=Monthly paymentInterest=924.81791.37=$133.43 Now, Oustanding Balance = Previous BalancePortion of payment reducing principal=146,100133.43=$145,966

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