Facebook Pixel How to Calculate the Weighted Average Interest Rate

How to Calculate the Weighted Average Interest Rate

Written by Mark Kantrowitz | Updated October 27, 2022

The interest rate on a Federal Direct Consolidation Loan is based on the weighted average of the interest rates on the loans included in the consolidation loan, rounded up to the nearest 1/8th of a percentage point. Learn how to calculate the weighted average interest rate.

What is a Weighted Average?

A weighted average interest rate is an average that is adjusted to reflect the contribution of each loan to the total debt. The weighted average multiplies each loan’s interest rate by the loan balance and divides the sum by the total loan balance. Each loan’s interest rate contributes to the weighted average in proportion to the loan’s percentage of the total debt.

For example, suppose you have two loans, $5,500 at 4.529% and $6,500 at 2.75%.

The simple average of the interest rates is (4.529% + 2.75%) / 2 = 3.6395%. But, the simple average assumes that each loan contributes equally to the overall interest rate.

Instead, the weighted average will adjust the average to reflect the fact that the 2.785% loan has a greater loan balance than the 4.529% loan.

To calculate the weighted average interest rate using this example, follow these steps.

Step 1: Multiply each loan balance by the corresponding interest rate

a. $5,500 x 4.529% = $249.095

b. $6,500 at 2.75% = $178.75

Step 2: Add the products together

a. ($5,500 x 4.529%) + ($6,500 at 2.75%) = $249.095 + $178.75 = $427.845

Step 3: Divide the sum by the total debt

$427.845 / ($5,500 + $6,500) = 3.565375%

Step 4: Round the result to the nearest 1/8th of a percentage point

Round (8 x 100 x 3.565375%) / (8 x 100) = 3.625%

The unrounded weighted average is slightly lower than the simple average, because the greater loan balance associated with the lower interest rate drags down the overall average.

The rounding of the weighted average up to the nearest 1/8th of a percentage point increases the interest rate slightly, by about 6 bp (0.06%).

If there are n loans with interest rates i and loan balances B, the weighted average interest rate is described by this formula, which uses the loan balances as weights on the interest rates:

weighted average interest rate  formula

Impact of the Weighted Average

There are several consequences of the formula for calculating the weighted average.

A loan with a higher loan balance will have a greater impact on the weighted average than a loan with a lower loan balance. The use of a weighted average causes loans with higher loan balances to contribute more to the overall weighted average.

The weighted average will always be between the highest and lowest interest rates on the loans included in the consolidation loan.

Thus, if a lender claims that the weighted average reduces the interest rate on a loan, that is misleading. The weighted average not only reduces the interest rate on the loan with the highest interest rate, but it also increases the interest rate on the loan with the lowest interest rate, unless all loans have the same interest rate.

The weighted average more or less preserves the cost of the loans.

Since a consolidation loan does not really change the cost of the loans, it does not save money.

The only way to save interest on a consolidation loan is by choosing a shorter repayment term. A shorter repayment term yields a higher monthly loan payment which pays off the debt quicker, thereby reducing the total interest paid over the life of the loan.

However, this only applies to federal direct consolidation loans. Borrowers who refinance student loans with a private lender may be able to lower their interest rate.

How Weighted Average Affects Loan Cost

To see how a weighted average affects the cost of the loans, consider the same two loans – $5,500 at 4.529% and $6,500 at 2.75% – with a 10-year repayment term.

These are the loan payments before consolidation:

  • $5,500 at 4.529% involves loan payments of
    $57.08 per month and $6,849.30 in total
  • $6,500 at 2.75% involves loan payments of $62.02
    per month and $7,442.01 in total

The sum of the loan payments is $119.10 per month and $14,291.31 in total.

These are the loan payments after consolidation:

  • $12,000 at 3.625% involves loan payments of
    $119.37 per month and $14,323.97 in total

That yields an increase of 27 cents per month and $32.66 in total payments.

A lot of the difference is due to the rounding up of the weighted average interest rate to the nearest 1/8th of a percentage point. This increases the costs slightly. Without rounding, the loan payments would be $119.03 per month and $14,283.73 in total, an increase of 7 cents per month and a decrease of $7.58 in total payments.

This particular example involves initial loan payments that are greater than the $50 minimum payment for Federal Direct Stafford Loans. If any of the loans had the monthly loan payments rounded up to $50, consolidation would have decreased the total monthly loan payments, thereby increasing the average repayment term and the total interest charged.

Was this article helpful?

About the author

Mark Kantrowitz is a nationally-recognized expert on student financial aid, scholarships and student loans. His mission is to deliver practical information, advice and tools to students and their families so they can make informed decisions about planning and paying for college. Mark writes extensively about student financial aid policy. He has testified before Congress and federal/state agencies about student aid on several occasions. Mark has been quoted in more than 10,000 newspaper and magazine articles. He has written for the New York Times, Wall Street Journal, Washington Post, Reuters, Huffington Post, U.S. News & World Report, Money Magazine, Bottom Line/Personal, Forbes, Newsweek and Time Magazine. He was named a Money Hero by Money Magazine. He is the author of five bestselling books about scholarships and financial aid, including How to Appeal for More College Financial Aid, Twisdoms about Paying for College, Filing the FAFSA and Secrets to Winning a Scholarship. Mark serves on the editorial board of the Journal of Student Financial Aid and the editorial advisory board of Bottom Line/Personal (a Boardroom, Inc. publication). He is also a member of the board of trustees of the Center for Excellence in Education. Mark previously served as a member of the board of directors of the National Scholarship Providers Association. Mark is currently Publisher of PrivateStudentLoans.guru, a web site that provides students with smart borrowing tips about private student loans. Mark has served previously as publisher of the Cappex.com, Edvisors, Fastweb and FinAid web sites. He has previously been employed at Just Research, the MIT Artificial Intelligence Laboratory, Bitstream Inc. and the Planning Research Corporation. Mark is President of Cerebly, Inc. (formerly MK Consulting, Inc.), a consulting firm focused on computer science, artificial intelligence, and statistical and policy analysis. Mark is ABD on a PhD in computer science from Carnegie Mellon University (CMU). He has Bachelor of Science degrees in mathematics and philosophy from MIT and a Master of Science degree in computer science from CMU. He is also an alumnus of the Research Science Institute program established by Admiral H. G. Rickover.

Full bio →

A good place to start:

See the best 529 plans, personalized for you

Helping families save for college since 1999
Join our email list

The latest articles and tips to help parents stay on track with saving and paying for college, delivered to your inbox every week.

Frequently featured in:

Saving For College is an unbiased, independent resource for parents and financial professionals, providing them with information and tools to understand the benefits of 529 college savings plans and how to meet the challenge of increasing college costs.

20533 Biscayne Blvd Ste 4 #199 Miami, FL 33180-1501Phone: (585) 286-5426Copyright © 2025 Saving for College, LLC. All Rights Reserved