The Effect of Interest Compounding on Unsubsidized Federal Loans

Attending college or university is a time-consuming process. Students have to contend with several expenses, such as tuition costs, living expenses, meal plans, transport, books, and stationery costs. This may lead to students and families looking for additional financial help. In this scenario, the knowledge of commercial math tips and tricks can help students and parents deal with financial dilemmas such as:

Should I look for loans to finance college?

How much can I borrow?

Should I go for a federal loan or a private loan?

What is the difference between subsidized and unsubsidized loans?

Do I have to repay a federal loan in full?

When does the repayment start?

What interest do I have to pay on a federal subsidized or unsubsidized loan? How is that interest calculated?

1. Financial Aid vs. Loan

Students should first scour the university website and other websites and institutions for scholarships and grants. It is best for a student to maximize special scholarships and grants because it is offered for free for academic pursuits. The scholarships, grants, and work-study earnings do not have to be repaid if you complete the term for which you received the money.

2. When is a Loan Required?

Students who still fall short of funds after exhausting the above options have to consider taking loans. Financial help in the form of loans is available from the federal government as well as private banks and lending institutions to help aspiring students achieve their academic and career goals.

3. Subsidized Loans vs. Unsubsidized Loans

When a person borrows money on loan from a bank or financial company, the borrowed money must be repaid with interest. It means the borrower is required to pay the money originally borrowed (principal) as well as the cost of using funds (interest) by way of repayment. The same is the case with federal loans. It is important to understand the fine print before opting for a loan to finance higher education.

Subsidized loans are based on financial need. For such loans, the federal government generally pays the interest that accrues while the borrower is pursuing higher education and during the grace period.

In the case of subsidized loans, the borrower has to repay only the principal and does not have to shoulder the burden of interest payments.

On the other hand, on unsubsidized loans, interest starts accruing right from the date of disbursement and continues throughout the life of the loan. And it is the borrower who is fully responsible for paying the interest as well as the principal amount regardless of the loan status.

4. Interest Rates on Federal Loans

Federal interest rates on student loans are fixed and do not vary on the basis of the personal financial history of the borrowing student. The interest rates are usually lower for undergraduate students and higher for graduate students and parents.

5. Simple Interest vs. Compound Interest

Simple interest loans charge interest only on the outstanding principal, whereas compound interest loans charge interest on the principal amount plus any unpaid interest. This makes the latter more expensive than simple interest loans. It also means that the amount you have to repay will be more than the amount you borrowed. For this reason, it is useful to know the math behind compounding so that you are aware of your repayment obligation.

For example, if your outstanding loan balance is $10,000, the interest rate is 2.75%, and the billing cycle is based on a monthly frequency, then:

Principal = $10,000

Rate of interest = 2.75%

Simple interest for one year = $10,000 x 2.75% = $275

Compounding of interest refers to the addition of unpaid interest to the principal balance of a loan to calculate future interest. If the interest gets added to the principal in the above example, it will result in higher interest amounts getting accrued on the loan in subsequent years. This means the borrower ends up paying interest on the principal as well as interest on interest. You can understand better by studying the following calculation:

Principal at the beginning of year 2 = $10,000 + $275 = $10,275

Rate of interest = 2.75%

Annual interest for year 2 = $10,275 x 2.75% = $282.56

Similarly, we can calculate the outstanding principal and interest amount for the next year and each subsequent year:

Principal at the beginning of year 3 = $10,275 + $282.56 = $10,557.56

Rate of interest = 2.75%

Annual interest for year 3 = $10,557.56 x 2.75% = $290.33

6. Effect of Compounding on Unsubsidized Federal Loans

Unsubsidized loans are governed by the terms and conditions decided at the beginning of the loan term.

This usually includes a grace period of repayment, which is 6 months, starting from one day after graduation. Some borrowers may be eligible to receive a deferment on the basis of being enrolled in college or university at least half-time or on account of economic hardship or unemployment. This is called the deferment period.

However, interest on unsubsidized loans is charged at all times – in-school, deferment, and grace periods – from the time the loan is disbursed until it is paid back in full. For payment of interest, the borrower has a choice: to pay the interest or allow it to accrue (accumulate) and be capitalized (that is, added to the principal amount of the loan balance).

In other words, if the interest on the unsubsidized federal student loan is not paid as it accumulates, its capitalization results in increasing the outstanding principal amount due on the loan. Interest then gets charged on that higher principal balance (principal plus accrued interest) due to compounding, which increases the loan’s overall cost. This may increase the monthly payment amount or the total number of installments payable by the borrower.

7. The Math Behind Increasing Outstanding Student Loan Balance

Using the earlier example, if the original loan balance is $10,000, the simple interest rate is 2.75%, no payments are made during the approximately 45-month period of undergraduate studies and the subsequent 6-month grace period (51 months), the amount of accrued interest at the beginning of the repayment period would be:

$10,000 x (0.0275/ 365 days) x 1,551 days = $1,169

This interest will be added to the principal, so the loan balance for repayment will become $11,169 ($10,000 + $1,169). If any repayment is missed or deferred, the amount of installment will further get added to the loan.

Let us try and consider a simplified real-life situation where the student borrows $5000 each of unsubsidized loans in the first, second, third, and fourth year of undergraduate study, and the interest rate remains the same.

  1. Amount borrowed in first year = $5,000

Rate of interest = 2.75%

Simple interest for 51 months = $5,000 x (0.0275 / 365 days) x 1,551days = $584.50 (a)

  1. Amount borrowed in second year = $5,000

Rate of interest = 2.75%

Simple interest for 39 months = $5,000 x (0.0275 / 365 days) x 1,186days = $446.78 (b)

  1. Amount borrowed in third year = $5,000

Rate of interest = 2.75%

Simple interest for 27 months = $5,000 x (0.0275 / 365 days) x 821days = $309.28 (c)

  1. Amount borrowed in fourth year = $5,000

Rate of interest = 2.75%

Simple interest for 15 months = $5,000 x (0.0275 / 365 days) x 456days = $171.78 (d)

At the end of the 51-month period, the outstanding student loan balance will become

$20,000 + (a) + (b) + (c) + (d) = $21,512.34

This amount will start accruing interest, and if the repayment schedule is not met, the accrued interest will further get added to the outstanding principal due to the effect of compounding, leading to even higher student debt.


The above points can serve as guidelines to keep in mind when calculating the effect of compounding on interest payments on all kinds of loans. However, the accumulated amount can change depending on the frequency of compounding. If the interest is compounded annually, we add the unpaid annual interest to the outstanding loan at the end of the year. If the compounding is monthly, the unpaid interest is added to the outstanding debt every month. In the case of some loans, the interest may be compounded daily, which means the unpaid interest keeps getting added to the principal on a daily basis.

To get a fair idea of other key points of commercial math tips and tricks, focus on understanding and building your knowledge of the concepts by taking advantage of Cuemath.


Helen is a multi-published, award-winning author of over 30 books, including the delightful Ivy & Bean series. She has written novels for young adults, including YA romantic comedies, and has written BBC drama.

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