Enter the principal loan amount, annual add-on (precomputed) interest rate, total loan term, and time elapsed into the calculator to estimate unearned (remaining) interest under a straight-line accrual assumption. (For amortizing loans where interest accrues on the declining balance, “unearned interest” is not calculated using this simple model.)
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Unearned Interest Formula
The following formula is used to estimate unearned interest for a precomputed/add-on simple-interest loan under a straight-line (pro-rata by time) accrual assumption. Some contracts and jurisdictions instead use the Rule of 78s or an actuarial method, which can produce different results.
UI = P * r * (n - t) = (P * r * n) - (P * r * t)
Variables:
- UI is the unearned interest ($)
- P is the principal loan amount ($)
- r is the annual add-on interest rate (decimal per year)
- n is the total loan term (years)
- t is the time elapsed (years)
To calculate the unearned interest in this model, compute the total precomputed interest over the full term (P · r · n), compute the earned interest to date (P · r · t), and subtract: UI = Total − Earned. (If you enter months or days, they are converted to years using months/12 and days/365.)
What Is Unearned Interest?
Unearned interest is the portion of a loan’s finance charge that has not yet been earned/recognized by the lender at a given point in time. It most commonly comes up with precomputed (add-on) loans, where the total interest for the full term is calculated upfront and then recognized over time. If a precomputed loan is paid off early, the borrower may be entitled to a rebate of the unearned portion of the finance charge; the exact earned/unearned split depends on the contract and applicable rules (e.g., straight-line, Rule of 78s, or actuarial methods).
How to Calculate Unearned Interest?
The following steps outline how to calculate the Unearned Interest using the given formula:
- First, determine the principal loan amount ($).
- Next, determine the annual add-on interest rate (decimal).
- Next, determine the total loan term (in years, or convert months to years by dividing by 12, and days to years by dividing by 365).
- Next, determine the time elapsed (in the same units as the total loan term, then convert to years if needed).
- Next, gather the formula from above = UI = P * r * (n – t).
- Finally, calculate the Unearned Interest.
- After inserting the variables and calculating the result, check your answer with a calculator.
Example Problem:
Use the following variables as an example problem to test your knowledge:
Principal loan amount ($) = 5000
Annual interest rate (decimal) = 0.05
Total number of periods (years) = 3
Number of periods elapsed (years) = 1
UI = P * r * (n – t) = 5000 * 0.05 * (3 – 1) = 500
Answer: The unearned interest remaining is $500 (under the straight-line add-on/precomputed interest assumption).
