Wednesday, August 23, 2017

Delayed Interest Rate Concessions on 20-Year Student Loans

Delayed Interest Rate Concessions on 20-Year Student Loans

Situation:   There has been a substantial increase in the number of elderly people with a student loan.   This problem will continue to worsen because the use of student loans continues to rise.  One way to mitigate issues pertaining to the growth of this problem is to require all future loans reduce interest rates to zero after a period, perhaps 12 years.

A second less modest proposal would involve interest rate reductions at a set time for people with relatively low income.

Question:  What are lifetime interest payments, of a $30,000 student loan with a 20-year maturity and an annual interest rate of 4.0 percent? 

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 despite the interest rate reduction.

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

How does the change in the contract impact the annual interest rate and lifetime interest payments?


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.


The balance on the student loan at the end of 144 months can be calculated through the FV function.  First use the PMT function to find the monthly payment on the loan is $181.79.   Then plug the monthly interest rate, number of periods, the monthly mortgage payment and the initial loan balance into 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 cumulative interest payments can be obtained by using the cumulative interest function to the first 144 payments.  (Remember all payments after 12 years go to reduction of principal.  We obtain:

-11092.62= =CUMIPMT(0.04/12,240,30000,1,144,0)

This cumulative interest payment can also be obtained by summing the monthly mortgage payments and subtracting the initial loan balance of $30,000

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 the IBR loan forgiveness program.

Certainly, a program that provides interest rate reductions for people based on their earning status 12 years after the initiation of a student loan would be less burdensome than the IBR program, which requires annual reviews.   Moreover, debt relief received under the IBR program is subject to federal income tax when received.   I suspect the debt relief from interest rate reduction would not be subject to federal income tax; although, the final decision on this point would be made by the U.S. Treasury.

Authors Note:  Readers who are interested in my work on student loan forgiveness and other aspects of education can go to the following post.  

A Pragmatic Education Agenda:

People who are interested in solving financial problems in Excel should go to the following post.

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