Data Source and Methodology
Authoritative source: Consumer Financial Protection Bureau (CFPB), “How is interest calculated on a loan?” (updated 2024). Direct link: consumerfinance.gov/ask-cfpb/how-is-interest-calculated-on-a-loan-en-1427/. All calculations strictly follow the formulas and guidance from this source.
Simple interest is computed only on the principal: I = P × r × t. This tool distributes total interest evenly across payments and assumes no compounding and no additional fees. Lender-specific rounding and day-count conventions may cause small differences.
The Formula Explained
Simple interest:
$$ I = P \times r \times t $$
Number of payments (rounded to the nearest whole payment):
$$ n = f \times t $$
Per-payment amount:
$$ \text{Payment} = \dfrac{P + I}{n} $$
Per-payment breakdown (simple equal split):
$$ \Delta P = \dfrac{P}{n}, \quad \Delta I = \dfrac{I}{n} $$
Total repaid:
$$ \text{Total} = P + I $$
How It Works: A Step-by-Step Example
Inputs: P = $10,000; r = 8% = 0.08; term = 3 years; frequency = monthly (f = 12, so n = 36).
1) Compute simple interest: I = P × r × t = 10,000 × 0.08 × 3 = 2,400.
2) Total to repay: P + I = 10,000 + 2,400 = 12,400.
3) Per-payment: Payment = (P + I) / n = 12,400 / 36 ≈ 344.44.
4) Split each payment evenly: ΔP = 10,000 / 36 ≈ 277.78, ΔI = 2,400 / 36 ≈ 66.67. Due to rounding to cents, the final payment may adjust by a few cents to match the exact total.