Comparing 15-year and 30-year Mortgages

Question One: A person is considering taking out a $180,000 mortgage and must choose between a 15-year FRM and a 30-year FRM.   The interest rate on the 15-year mortgage is 2.90 while the interest rate on the 30-year mortgage is 3.40.

What are the monthly payments on the two loans?

What are the total interest payments on the two loans over the life of the loan?

What is the after-tax cost of the interest payments on the two loans?

What is the tax savings from the tax deductibility of mortgage interest?

What is remaining loan balance after 15 years for the two loans?

Answer: The monthly mortgage payment calculation is directly calculated from the PMT function in Excel.  The variables inputted into the PMT function are the interest rate, the term and the loan balance.

The lifetime interest cost is calculated two ways.   The first way involves noting that the difference between total payments and the repaid loan balance is equal to interest payments. (180* $1234-$180,000) =$42,193.

The second way involves calculating cumulative interest payments directly from the CUMIPMT function in Excel. Put Rate=0.029/12, NPER=180, PV=$180,000 STARTPERIOD=1, ENDPERIOD=180, and Type=0 into CUMIPMT and get $42,193.)

The after tax cost of interest payments is (1-MTR) x INTEREST.

The tax savings from interest payments is MTR x INTEREST

The mortgage balance after 15 years is obtained directly from the FV function in Excel. Note FV (RATE=0.029/12,NPER=180, PMT=-1234,PV-180000) is equal to $0. This is a good way to check your work since the balance on a 15-year mortgage held for 15 years must be $0.

The complete answers are laid out in the table below.

A Comparison of 15-year and 30-year FRM
15-year FRM 30-year FRM Notes
Rate 0.029 0.034 Assumption
Period 180 360 Assumption
Loan $180,000 $180,000 Assumption
Payment -$1,234 -$798 Calculation From Payment Function
Interest Cost Calculation One $42,193 $107,376 Calculation: Total Payments – Loan Balance
Interest Cost Calculation Two $42,193 $107,376 Calculation From CUMIPT Function
Marginal Tax Rate 0.3 0.3 Assumption
After Tax Interest Cost $29,535 $75,163 Calculation: (1-mtr)*Interest Cost
Tax Savings from Mortgage Deductibility $12,658.05 $32,212.75 Tax Savings from Mortgage Deduction
Mortgage Balance After Fifteen Years $0 -$112,435 Calculation: From FV Function
Total Mortgage Payments Over 15 Years -$222,193 -$143,688 Calculation 180*MONTHLY MORTGAGE PAYMENT

Discussion of Comparison of 15-year and 30-Year FRM:

  • Over a 15-year period the homeowner with the 30-year FRM has accumulated $112,435 less house equity than the homeowner with the 15-year FRM.
  • Over the 15-year period, the homeowner with the 15-year mortgage has paid over $78,000 more in mortgage payments than the homeowner with the 30-year mortgage. However, the owner with the 30-year mortgage is not done yet.
  • The additional tax savings from the use of the 30-year FRM is around $20,000.

 

Authors Note:   People interested in what will happen to the Affordable Care Act under Trump should go to my health care blog on the topic.

Here is a post on Senator Paul’s health care plan.

http://healthcarememos.blogspot.com/2017/01/senator-rand-pauls-health-care-plan.html

My own outline of potential modifications to the ACA will be presented shortly.

 

 

Increases in Undergraduate Debt 2003/2004 to 2011/2012

The statistics presented in this post document the dramatic increase in student debt between 2004 and 2012.

Increases in Undergraduate Debt 2003/2004 to 2011/2012

 

My holiday visit with in-laws included less discussion of politics this year for obvious reasons but I did have a brief discussion on student debt with one relative.   His view of the issue is that since his generation paid for their college no additional cost subsidies are needed. My concern is that the recent increases in costs are having substantial adverse impacts on the current cohort of students.

 

I am planning several more posts on college costs and their economic and impacts.   This post looks at the trend growth of student debt between the 2003/2004 and the 2011/2012 academic years.

 

The Data: The source of data for this study is the NSPAS database. I was able to access the data from the NCES Power Statistics Portal.

 

https://nces.ed.gov/datalab/index.aspx

 

My variable of interest in this post is cumulative amount borrowed in the undergraduate years by people receiving a bachelor’s degree at four-year institutions.   I have presented separate tables for private and public four-year institutions.
Three statistics are presented – Average debt for borrowers, the percent of students who borrowed, and the percent of students who borrowed more than $25,000.

 

The data does not include information on borrowing by parents through the PLUS program.

 

Statistical Results:

 

The statistics describing change in cumulative student debt are presented in the table below.

 

Cumulative Under Graduate Student Debt at Four-Year Institutions

2004 to 2012

Bachelors Degree Four-Year Public
2003/2004 2011/2012 Diff. % Diff.
Average Debt for Borrowers $11,958 $18,845 $6,887 57.6%
% of Students who Borrowed 56.6 63.5 6.9 12.1%
% of Students with debt greater than $25,000 5.3 16.9 11.6 218.7%
Bachelors Degree Four-Year Private
2003/2004 2011/2012 Difference % Diff
Average Debt for Borrowers 14,536 22,962 $8,426 58.0%
% of Students who Borrowed 66.9 69.1 2.2 3.3%
% of Students with debt greater than $25,000 9.6 22.9 13.3 138.0%
Both Public and Private Four-Year Programs
Average Debt for Borrowers 12,876 20,163 $7,287 56.6%
% of Students who Borrowed 60.8 65.2 4.4 7.2%
% of Students with debt greater than $25,000 6.8 18.7 11.9 176.4%

 

 

Summary of Statistical Results:

 

The growth of cumulative student debt among people receiving a bachelor’s degree from a four-year institution was tremendous during this brief eight-year period.

 

 

Total debt incurred by student borrowers receiving a bachelor’s degree rose by around 57% over this eight year period.

 

The proportion of undergraduate bachelor degree students incurring debt rose by 6.9 percentage points at public institutions and 2.2 percentage points at private institutions.

 

The proportion of undergraduate bachelor degree students incurring more than $25,000 in debt went from 5.3% to 16.9 percent for students at public schools and from 9.6 percent to 22.9 percent for students at private institutions.

 

Other Student Debt Trends

 

These issues will be addressed in future posts.

 

The expansion of PLUS loans to parents:

 

Increases in the use of private debt:

 

Changes in debt incurred by graduate students:

 

Changes in the number of students with excessive levels of student debt:

 

 

Economic Financial and Social Implications:

 

 

Economic issues related to the increase in student debt include – (1) A decision by many young people to live with parents and delays in starting a family, (2) a decision to delay home purchases, (3) the choice between a 30-year and 15-year mortgage, and (4) a decision to delay placing funds in a 401(k) plan.

 

Many older financial experts do not agree with the decision by many in the current generation to delay home purchases and delay saving for retirement.

 

My view is that the older generation is not in fully touch with the economic realities facing many in the millennial generation from the explosion in student debt occurring over a mere eight years.

 

I am planning a lot more empirical work on this issue.

 

PREVIOUS WORK:

 

Some of my previous work examines proposal to provide financial relief to some debtors who get over their head in debt. Here are some examples:

 

 

Seven Ways to Provide Debt Relief:

http://betterworldpolicies.blogspot.com/2016/09/seven-ways-to-provide-student-debt.html

 

Is IBR the best way to provide student loan debt relief:

http://betterworldpolicies.blogspot.com/2016/09/is-ibr-best-way-to-provide-student-loan_8.html

 

 

In addition, I have a short book on Kindle on managing debt and the impact of debt on lifetime savings.

 

The Nine Essays on Debt and Your Retirement:

http://amzn.to/2iYe1iV