How to Calculate the Effective Interest Rate on a Flat-Rate Loan
A flat rate charges interest on the original amount for the whole term, so on a loan repaid in equal installments the rate on the balance actually owed is close to double the quoted rate.
The Flat-Rate Loan Interest formula
Calculator
Enter the loan size, the quoted flat rate and the term to see what the borrower really pays on the balance owed.
What the borrower receives at the start of the loan.
Charged on the original amount for the whole term, whatever has been repaid.
Length of the loan, repaid in equal monthly installments.
Measured against the money actually outstanding the loan costs 36.9% a year, which is what to compare with a declining-balance quote.
- Total interest charged
- $100
- Total repaid
- $600
- Each monthly installment
- $50
- Average balance still owed
- $270.83
- Times the quoted flat rate
- 1.85×
The flat rate applies to the original amount for the whole term, so interest comes to $100 however fast the loan is repaid.
Principal plus interest means $600 leaves the borrower's hands over the term.
Total repayment split evenly is $50 a month, part principal and part interest.
The balance falls with every payment, so on average only $270.83 is outstanding, a little over half the amount borrowed.
The true cost is 1.85 times the quoted rate, because the average balance is that much smaller than the amount the interest was charged on.
How to calculate Flat-Rate Loan Interest, step by step
- 1Work out the total interest. A flat rate is charged on the original amount for every period of the loan, so total interest = amount borrowed × flat rate × years, no matter how much has already been repaid.
- 2Split the total into equal installments. Add the interest to the principal and divide by the number of payments. Every installment mixes a slice of principal with a fixed slice of interest.
- 3Find the average balance still owed. The balance falls with each payment, from the full amount down to almost nothing, so the average outstanding is the amount borrowed × (n + 1) ÷ (2n), a little over half the loan.
- 4Divide the interest by what was really owed. Effective rate = total interest ÷ (average balance × years) × 100. Because the average balance is roughly half the principal, the answer comes out near twice the quoted flat rate.
Worked example: Flat-Rate Loan Interest
A microlender offers $500 at a flat rate of 20% a year, repaid in 12 equal monthly installments. Total interest = $500 × 0.20 = $100, so the borrower repays $600 in installments of $50. The balance falls with every payment, and the average amount owed across the year is $500 × 13 ÷ 24 = $270.83. Charging $100 of interest on that average balance is a rate of 100 ÷ 270.83 = 36.9% a year, about 1.85 times the quoted rate. A lender quoting 20% flat and one quoting 36% on the declining balance are charging almost the same thing.
Flat-Rate Loan Interest questions
Why is the flat rate so much lower than the true rate?
Because it is charged on the amount originally borrowed rather than the amount still owed. By the final month the borrower has repaid most of the principal but is still paying interest calculated on all of it, so the same dollars of interest sit on a much smaller balance.
Is the effective rate always exactly double the flat rate?
Close, but not exactly. With n equal installments the average balance is (n + 1) ÷ (2n) of the principal, so the multiple is 2n ÷ (n + 1). At 12 installments that is 1.85, and it creeps toward 2 as the number of installments rises.
Why do lenders quote flat rates at all?
They are simple to administer and simple to explain: the installment never changes and the interest is one multiplication. The cost to the borrower is that a flat quote looks far cheaper than the declining-balance rate it corresponds to, so comparing two loans means converting both to the same basis first.
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