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Unearned Interest by Actuarial Method Converter

This calculator helps determine the unearned interest on a loan using the actuarial method. It's useful for lenders and borrowers who want to understand how much interest is yet to be earned based on the current loan balance. The result adjusts based on how much of the loan has been repaid, using a compounding ratio.

Calculate Unearned Loan Interest Using Actuarial Formula

Input Fields
A
$
Enter the initial amount of the loan
I
$
Enter the total finance charge or interest
R
$
Enter the remaining balance on the loan
k
Adjustment exponent, usually between 1 and 2
If enabled, the result will update automatically when you change any value.

Actuarial Unearned Interest Formula

Formula
$$\text{Unearned Interest} = \text{Total Interest} \times \left( \frac{\text{Remaining Balance}}{\text{Original Loan Amount}} \right)^{k} $$

Where:

  • Total Interest – the total amount of interest on the loan
  • Remaining Balance – current unpaid principal
  • Original Loan Amount – the full original loan principal
  • k – the number of remaining payment periods (usually months)


The actuarial method is commonly used in amortized loans to compute how much interest is “unearned” if the loan is paid off early. It assumes a proportional decrease in interest over time, adjusted for compounding. The exponent k reflects how far into the loan schedule you are. For example, in a 24-month loan with 6 months remaining, k = 6. This approach is more precise than the rule of 78s and favors the borrower.

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One thought on “Unearned Interest by Actuarial Method Converter”

  1. Elly-May O'Toole says:
    10.02.2020 at 19:34

    I am trying to calculate the cost of buying back 3 years of service from 40 years ago. My salary was 10,000 per year. That would have been about 3300 unpaid contribution and they say actuarial interest of 7.25% for 40 years. I cannot find out how to calculate this.

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