Ssac2006.Hf5691.Jm1.1 Student

7/28/2019 Ssac2006.Hf5691.Jm1.1 Student

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Understanding MortgagePayments I am going to pay

HOW MUCH for this house?

You borrow for your first home but that is NOT the amount of money

you are going to have to pay back.You will be paying back MUCH

MORE. Why? Do you know how to calculate how much more you

will have to pay?

Prepared for SSAC byJody Murphy Colby-Sawyer College

The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2006

Supporting Quantitative conceptsand skillsForward modeling

PercentagesVisual display of dataColumn graphs

SSAC2006.HF5691.JM1.1

1

Core Quantitative conceptMultivariable function


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You find the home of your dreams.Assuming you are still in your home atthe end of the mortgage, and have not

refinanced, how much did thismortgage really cost you?

Problem

The purchase price of the home is $250,000. To avoid PMI you makea down payment of 20% and finance the balance. Your bank offers a

7% fixed rate 30-year mortgage. Calculate the required monthlypayment and create an amortization table.

3


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Calculating Mortgage Payments: Worksheet facts

Create the spreadsheet below by utilizing the facts in the problem.

= Cell with a number in it

= Cell with a formula in it

Color convention throughout this module

This is the first spreadsheet to create. You will beexpanding this spreadsheet as needed.

B C2 Home Purchase Information:3 purchase price of home: 250,000.00$4 20% down payment: 50,000.00$5 amount to finance: 200,000.00$67 Mortgage Information:8 term: 30 year mortgage9 months: 360

10 interest rate: 7%11 mortgage : 200,000.00$


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Calculating Mortgage Payments: Payment Calculation mathematically

Your monthly payment amount will depend on the size of the mortgage, theinterest rate, and how many months you will make payments. In other words,your monthly payment ( PMT ) is a function of the principal ( P ), the interest rate ( r ),and the number of payments ( n). Mathematically, this is expressed as

PMT = PMT (P , r , n)

PMT is a multivariable function . The values of P , r , and n, which are in theparentheses, are the arguments of the function. Specifically, here is the function:

Please note r is expressed as a percent (.07 per year, not 7 per year), and that n is the number in months. If that were not the case, there would be some other value than 12 in the equation.

)1)12

1((*12

)12

1(**

n

n

r

r r P

PMT

You may be happy to know that there is a built-in Excel function (PMT) thatcalculates the function for you. We will use that function in this module.

What would this equation be if you wanted to express r as 7instead of .07?


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Calculating Mortgage Payments: Payment Calculation using Excel

Using the PMT function in Excel determine your monthly mortgagepayment.

You can insert the PMT function bygoing to Insert, Function, PMT, and

following the instructions as providedby Excel.

B C D E2 Home Purchase Information:3 purchase price of home: 250,000.00$4 20% down payment: 50,000.00$5 amount to finance: 200,000.00$

67 Mortgage Information:8 term: 30 year mortgage9 months: 360

10 interest rate: 7%11 mortgage : 200,000.00$1213 Monthly Payment: 1,330.60$ using PMT function


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Calculating Mortgage Payments: Interest and Principal Components

Expand your spreadsheet to include the setup for the amortization table of the mortgage for month zero (for reference). You will note at month zero

your remaining balance is the full value of your mortgage and your equity isthe amount of your down payment.

+F16 =+C18-D18

B C D E F G2 Home Purchase Information:3 purchase price of home: 250,000.00$4 20% down payment: 50,000.00$5 amount to finance: 200,000.00$67 Mortgage Information:8 term: 30 year mortgage9 months: 36010 interest rate: 7%11 mortgage : 200,000.00$1213 Monthly Payment: 1,330.60$ using PMT function1415

16 month payment interest principal remaining balance equity17 0 200,000.00 50,000.00$


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Expand your spreadsheet to include the calculations of interest andprincipal breakdown for the first payment month of the loan.

+C$13

=(+F17*C$10)/12 =+C18-D18

B C D E F G2 Home Purchase Information:3 purchase price of home: 250,000.00$4 20% down payment: 50,000.00$5 amount to finance: 200,000.00$67 Mortgage Information:8 term: 30 year mortgage9 months: 36010 interest rate: 7%11 mortgage : 200,000.00$1213 Monthly Payment: 1,330.60$ using PMT function141516 month payment interest principal remaining balance equity17 0 200,000.00 50,000.00$18 1 1,330.60$ 1,166.67$ 163.94$


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Expand your spreadsheet to show the changes in remaining balance andequity after applying the first months payment.

=+F17-E18=+G17+E18

B C D E F G2 Home Purchase Information:3 purchase price of home: 250,000.00$4 20% down payment: 50,000.00$5 amount to finance: 200,000.00$67 Mortgage Information:

8 term: 30 year mortgage9 months: 360

10 interest rate: 7%11 mortgage : 200,000.00$1213 Monthly Payment: 1,330.60$ using PMT function141516 month payment interest principal remaining balance equity17 0 200,000.00 50,000.00$18 1 1,330.60$ 1,166.67$ 163.94$ 199,836.06$ 50,163.94$


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B C D E F G2 Home Purchase Information:3 purchase price of home: 250,000.00$4 20% down payment: 50,000.00$5 amount to finance: 200,000.00$67 Mortgage Information:8 term: 30 year mortgage9 months: 36010 interest rate: 7%11 mortgage : 200,000.00$1213 Monthly Payment: 1,330.60$ using PMT function141516 month payment interest principal remaining balance equity17 0 200,000.00 50,000.00$18 1 1,330.60$ 1,166.67$ 163.94$ 199,836.06$ 50,163.94$19 2 1,330.60$ 1,165.71$ 164.89$ 199,671.17$ 50,328.83$20 3 1,330.60$ 1,164.75$ 165.86$ 199,505.31$ 50,494.69$

21 4 1,330.60$ 1,163.78$ 166.82$ 199,338.49$ 50,661.51$22 5 1,330.60$ 1,162.81$ 167.80$ 199,170.69$ 50,829.31$23 6 1,330.60$ 1,161.83$ 168.78$ 199,001.91$ 50,998.09$24 7 1,330.60$ 1,160.84$ 169.76$ 198,832.15$ 51,167.85$25 8 1,330.60$ 1,159.85$ 170.75$ 198,661.40$ 51,338.60$26 9 1,330.60$ 1,158.86$ 171.75$ 198,489.66$ 51,510.34$27 10 1,330.60$ 1,157.86$ 172.75$ 198,316.91$ 51,683.09$28 11 1,330.60$ 1,156.85$ 173.76$ 198,143.15$ 51,856.85$29 12 1,330.60$ 1,155.84$ 174.77$ 197,968.38$ 52,031.62$


Expand your spreadsheet to include the next 11 of payments or thefirst full year of payments.

=B18+1

Highlight the cellyou would like

to copy.Edit

CopyHighlight the cell

you would liketo copy to.

EditPaste


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B C D E F G2 Home Purchase Information:3 purchase price of home: 250,000.00$4 20% down payment: 50,000.00$5 amount to finance: 200,000.00$67 Mortgage Information:8 term: 30 year mortgage9 months: 360

10 interest rate: 7%11 mortgage : 200,000.00$1213 Monthly Payment: 1,330.60$ using PMT function141516 month payment interest principal remaining balance equity17 0 200,000.00 50,000.00$18 1 1,330.60$ 1,166.67$ 163.94$ 199,836.06$ 50,163.94$19 2 1,330.60$ 1,165.71$ 164.89$ 199,671.17$ 50,328.83$20 3 1,330.60$ 1,164.75$ 165.86$ 199,505.31$ 50,494.69$369 352 1,330.60$ 67.86$ 1,262.74$ 10,370.76$ 239,629.24$370 353 1,330.60$ 60.50$ 1,270.11$ 9,100.65$ 240,899.35$371 354 1,330.60$ 53.09$ 1,277.52$ 7,823.13$ 242,176.87$372 355 1,330.60$ 45.63$ 1,284.97$ 6,538.16$ 243,461.84$

373 356 1,330.60$ 38.14$ 1,292.47$ 5,245.70$ 244,754.30$374 357 1,330.60$ 30.60$ 1,300.01$ 3,945.69$ 246,054.31$375 358 1,330.60$ 23.02$ 1,307.59$ 2,638.10$ 247,361.90$376 359 1,330.60$ 15.39$ 1,315.22$ 1,322.89$ 248,677.11$377 360 1,330.60$ 7.72$ 1,322.89$ 0.00$ 250,000.00$


Expand your spreadsheet to include the remaining months of theloan (up to 360 months). Confirm that the remaining balance is zero

at month 360.

This must be zero. The mortgageis fully paid at month 360 (30 years

* 12 months).

Your

spreadsheetwill have all 360months. Thisexample hasrows hidden

due tospreadsheetsize.


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B C D E F G

2 Home Purchase Information:3 purchase price of home: 250,000.00$4 20% down payment: 50,000.00$5 amount to finance: 200,000.00$67 Mortgage Information:8 term: 30 year mortgage9 months: 36010 interest rate: 7%11 mortgage : 200,000.00$1213 Monthly Payment: 1,330.60$ using PMT function

141516 month payment interest principal remaining balance equity17 0 200,000.00 50,000.00$18 1 1,330.60$ 1,166.67$ 163.94$ 199,836.06$ 50,163.94$19 2 1,330.60$ 1,165.71$ 164.89$ 199,671.17$ 50,328.83$20 3 1,330.60$ 1,164.75$ 165.86$ 199,505.31$ 50,494.69$

369 352 1,330.60$ 67.86$ 1,262.74$ 10,370.76$ 239,629.24$370 353 1,330.60$ 60.50$ 1,270.11$ 9,100.65$ 240,899.35$371 354 1,330.60$ 53.09$ 1,277.52$ 7,823.13$ 242,176.87$372 355 1,330.60$ 45.63$ 1,284.97$ 6,538.16$ 243,461.84$373 356 1,330.60$ 38.14$ 1,292.47$ 5,245.70$ 244,754.30$374 357 1,330.60$ 30.60$ 1,300.01$ 3,945.69$ 246,054.31$375 358 1,330.60$ 23.02$ 1,307.59$ 2,638.10$ 247,361.90$376 359 1,330.60$ 15.39$ 1,315.22$ 1,322.89$ 248,677.11$377 360 1,330.60$ 7.72$ 1,322.89$ 0.00$ 250,000.00$378379380 Total Payments 479,017.80$381 Total Interest Paid Over Life of Loan 279,017.80$382 Total Principal Paid Over Life of Loan 200,000.00$


Expand your spreadsheet to include totals for the following three columns:payment, interest, and principal.

Wow! For your $200,000 mortgage you would actually pay more for interestthan the amount of the original loan!

=SUM(C18:C377)


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Calculating Mortgage Payments: Chart for the first year

Create a column chart for the first year of mortgage payments.

Look at all that yellow! Most of each monthlypayment is applied to interest, not to principal.

Highlight Month, Interest and Principal for the first year. Select Insert andChart. This will open the chart wizard. Select Column, Stacked Column,

and continue using the Chart Wizard until chart is complete.

First Year Payment Mix

$0$100$200$300$400$500$600

$700$800$900

$1,000$1,100$1,200$1,300

1 2 3 4 5 6 7 8 9 10 11 12

Month

P e r c e n t a g e

principal

interest


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Calculating Mortgage Payments: Chart for the life of the mortgage

Create a chart of the mortgage payments for the life of the mortgage.

Hint: eliminate borders and choose bright colors to clearly see chart.

As time goes on, more and more of the payment is appliedto principal.

Mortgage Payment Mix

$-$100$200$300$400$500$600$700$800$900

$1,000$1,100$1,200$1,300$1,400

1 2 3 352 353 354 355 356 357 358 359 360

Month

D o

l l a r A m o u n

t

principalinterest


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End of Module Assignment

1. Write a short paragraph on how mortgage payments are applied.

2. Using the facts from the original worksheet decrease the interest rateto 6%. Citing specific numerical values discuss how the change inthe interest rate affects the total cost of the mortgage.

3. Using the facts from the original worksheet reduce the term to 15years. Citing specific numerical values discuss how the change in theterm affects the total cost of the mortgage.

4. Using the facts from the original worksheet, and assuming noprepayment penalties, increase your monthly payment by $100.Citing specific numerical values discuss how the change in thepayment affects the total cost of the loan.

Continue on the next page.


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End of Module Assignment

5. Imagine that you have graduated college, landed a great job and are ready tobuy your first home. Research average starting salaries in your field. Usingprint or computer real estate listings find a home (house, condominium, etc.)that you would like to buy near your new job. Please cut out or print out thead for the home. Find a local (your geographical area) bank offering 30 year fixed rate mortgages. Compare local bank mortgage offerings to mortgagesfound by utilizing www.bankrate.com .

6. Assume you will be putting down 20% and financing the balance on your home. Using the PMT function in Excel determine your monthly payment. Is it

reasonable based on the average starting salaries in your field? If so, shouldyou consider other options to pay off your mortgage quicker? If not, whatother feasible options are available?

7. Using an Excel spreadsheet create an amortization table for the mortgage thatbest fits your personal situation.

8. Create a chart illustrating the components of your mortgage payments for thelife of the mortgage.

9. The Federal Open Market Committee is scheduled to meet shortly, should yoube concerned about locking in your interest rate? Why or why not?
http://www.bankrate.com/http://www.bankrate.com/


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Definitions

PMI Principal mortgage insurance. Insurance that usually needs tobe paid when you put less than a 20% down payment on a house.

Return to presentation.


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Hints for using the PMT function within Excel

Rate - the interest rate for the mortgage per month. If the rate isstated as an annual rate it must be divided by 12 months.

Nper - the number of payments to be made for the mortgage.

Pv - the present value of the mortgage. The amount that is beingfinanced.

Fv - the future value of the mortgage. After all payments are madethe mortgage balance is expected to be zero.

Type - when the mortgage payments are expected to be made, 1indicates at the beginning of the period and 0 indicates at theend of the period. Return to presentation.

Ssac2006.Hf5691.Jm1.1 Student

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