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?

**Analysis**:

**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.

-13630.58=CUMIPMT(0.04/12,240,30000,1,240,0)

**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.

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

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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