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:
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.
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.