Tuesday, May 21, 2019

Delayed Interest Rate Concessions on 20-Year Student Loans

There has been a substantial increase in the number of elderly people with a student loan.  This post uses Excel finance functions to evaluate a student loan, where interest rates are cut to 0 after 12 years of payments.

Question:  Consider a student with a 20-year $30,000 student loan at 4.0% interest.

What is the monthly payment on the student loan?

What are lifetime interest payments on this loan?

The government decides to lower the interest rate to 0 percent after 12 years.  The loan contract requires the borrow to continue with initial payments on the loan after the interest rate reduction.

What are the lifetime interest payments on the modified loan?

How many months does it take for the borrower to completely repay the loan under the new loan contract? 


Discussion of traditional 20-year student loan:   The payment on the 20-year loan is obtained from the payment function in Excel. 

$181.79 = PMT(0.04/12,240,-30000)

The cumulative interest payments are the sum of all monthly payments minus the initial loan balance of $30,000.   This figure is $13,360.58.  

This figure can be obtained directly from the CUMIPMT function.


Discussion of the modified student loan contract:   

The amount of interest on the student loan when the interest rate is set to 0 percent after twelve years can be calculated directly from the CUMIPMT function by recognizing that all interest payments cease after 144 moths.


This is the total interest on the loan since no interest is charged after year 12.

The balance on the student loan at the end of 144 months can be calculated through the FV function. 

$14,914.27 =FV(0.04/12,144,181.79,-30000)

At a 0 percent interest rate, the entire payment goes towards principal.   The number of additional months after 12 years where payment ends is 82.04 (14,917.62/181.79).

The loan with the interest concession after 12 years is repaid in 226 payments.   (144+82).   I added $7.15 to the final payment to account for the fraction over 82 months.

The annual rate of return can be obtained by taking the IRR of 227 payments (the initial loan balance of -30,000 followed by the 226 (144+82.04) monthly payments.) The monthly IRR from these cash flow streams is 0.294%

Multiply by 12 to get the annual interest rate on the loan with the interest concession after 12 year to get 3.53 %

Summary of Results:   Reducing interest rates on this 20 percent student loan to 0 after 12 years will reduce the average annual interest rate received by investors from 4.0 percent to 3.53 percent.   The interest reduction will also reduce the maturity of the loan from 20 years to 18.84 years. 

Policy Discussions:  The figures presented in this post assume all payments are made as scheduled.   It is possible that some people will stop payments once interest rates are set to 0 percent because they would prefer to pay higher interest rate loans.   This could be deterred by reporting these people to credit bureaus.   It is also possible that some people who are having trouble making payments will simply give up if they do not receive some debt relief. 

Lenders tend to oppose any form of loan forgiveness.   However, I believe that lenders would prefer this type of interest concession to Income Based Replacement loan programs where debt is actually discharged.

Authors Notes:   Please consider my book

Innovative Solutions to the College Debt Problem:

Monday, May 20, 2019

Modeling Choice between a Jumbo and Conventional Mortgage

This post describes a problem that I was recently asked to analyze.   An applicant for a mortgage refinance had to choose between refinancing the entire current mortgage with either a jumbo loan or a small conventional loan and a cash paydown.  He needed my advice on what option was best.

Question:  A person refinancing a $650,000 30-year Adjustable Rate Mortgage loan into a 15-year Fixed Rate Mortgage has two options.   The first option involves refinancing the current $650,000 30-year ARM with a $650,000 jumbo 15-year FRM.   The second option involves reducing the loan balance by $100,000 and taking out a $550,000 conventional FRM.

Note many people lack an extra $100,000 and don’t have two options.

The advantages of the jumbo loan are greater liquidity and earnings on the $100,000, which is invested in financial assets.

The advantage of the conventional loan is lower lifetime interest payments.

Create a spreadsheet to evaluate these two options for base case assumptions and for modifications to the base case.

The Base Case:

Both mortgages have a 3.75% interest rate,

Invested funds under the jumbo bond option are invested in Treasury bills and receive a 2.5% rate of return,

The marginal tax rate applied to both investment income and gains from mortgage interest deduction is 30%.

What option – the jumbo mortgage or the conventional mortgage – is preferable under the base case assumption?

Alternative Scenarios:

Often conventional mortgage interest rates are lower than jumbo interest rates.    Assume the conventional mortgage interest rate is 3.25% and the jumbo mortgage interest rate is 3.75%.  
What option is preferable?

The investor chooses to invest partially in stock and partially in Treasury bonds.   Accounting for risk, the certainty equivalent rate of return on invested funds is 6.5%.  Assume a 3.25% conventional interest rate and a 3.75% jumbo interest rate   What option is preferable?


The measure  of the most affordable mortgage is  after-tax lifetime interest costs minus after tax investment income plus

Here is a table describing base case results.

Base Case Results
Jumbo Loan No Paydown
Conventional Loan $100,000 Paydown
Interest Rate
Loan Term Years
Paydown Amount
Initial Loan Balance
Invested Cash
Interest Rate on Invested Cash
Monthly Mortgage Payment
Mortgage Payments over 15 years
Annual Earnings On Cash Invested
Cumulative Earnings
Mortgage Payments - Cumulative Earnings
Cumulative Interest
Total Payments
Tax  Rate
Tax Savings from Deduction of Mortgage Interest
Tax Paid on  Investment Income
After Tax Mortgage Payments Minus After Tax investment Income

·      The conventional mortgage appears to save the home buyer around $95,000 ($762k- $667k )over fifteen years.    This is a bit more than $6,300 per year.

Lower conventional mortgage interest rates

Typically interest rates on conventional mortgages can be lower than interest rates on jumbo mortgages.   The differential is currently fairly small because demand for large houses is at this time lower than demand for mid-size houses.  

The results below pertain to a situation where the conventional mortgage interest rate is 3.25%, the jumbo mortgage interest rate is 3.75% and all other variables are set by base rate assumptions.

Lower Conventional Mortgage Rate Results
After Tax Mortgage Payments Minus After Tax investment Income
Assumed Conventional Mortgage has 3.25% interest all other assumptions are base case

·      The conventional option appears to save the borrower close to $112,000 over $9,300 per year.

Lower Conventional Mortgage Rates  

A person who takes out the jumbo loan and invests in stocks could get higher returns. The final scenario assumes a 6.5% return, a conventional mortgage rate of 3.25%, a jumbo rate of 3.75% and all other variables determined by the base case. 

Higher Returns & Lower Conventional Mortgage Rates
After Tax Mortgage Payments Minus After Tax investment Income

·      The conventional option appears to save the borrower around $53,000 or around $3,500 per year. 

Concluding Remarks:   The conventional loan & pay down option beats the jumbo loan option in all three scenarios considered here.   The jumbo loan option could win after the fact if borrower buys risky assets and these assets experience large returns but this scenario does not consider risk. 

The best justification for the jumbo loan option would be fear of losing so much liquidity.  

Authors Note:   Please consider my books on Kindle.

Defying Magnets:  Centrist Policies in a Polarized World.

Innovative Solutions to the College Debt Problem

Things to Consider Before Purchasing Long Term Care Insurance