Effective Borrowing Rate with Fees
Effective Borrowing Rate with Fees
The annual rate a borrower actually pays once up-front fees are counted: the rate that makes the scheduled payments worth the loan net of fees. This is the idea behind the APR quoted on loan disclosures.
When to use: Use to compare a low-rate loan with high fees against a higher-rate loan with none. The effective rate puts them on one footing.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| EffRate | Effective Rate | Annual rate implied by the net proceeds | % |
| PV | Loan Amount | Face amount of the loan | $ |
| Fees | Upfront Fees | Origination and other fees deducted at closing | $ |
| PMT | Payment | Scheduled periodic payment | $ |
| n | Loan Term | Term in years | years |
| m | Payments per Year | Number of payments per year | integer |
Real-Life Examples
Example 1: Mortgage with 2% in Fees
A $300,000 30-year mortgage at a 6.5% note rate ($1,896.20 a month) with $6,000 of fees. Effective rate?
Given
Step-by-Step
The fees add about 20 basis points to the true cost. That is the gap between the advertised rate and the APR on the disclosure.
Example 2: Car Loan with a $500 Fee
A $25,000 five-year car loan at 7% ($495.03 a month) with a $500 origination fee.
Given
Step-by-Step
A fee of 2% of the loan raises the effective rate by 85 basis points on a short loan. Fees hurt more the shorter the term, because there is less time to spread them over.
Frequently Asked Questions
It is the core of it. Regulatory APR definitions specify exactly which fees count and how; this formula takes whatever fees you enter and solves the same equation.
The fee is a fixed cost spread across fewer payments, so each payment carries more of it.