Loan amortization

Each row begins with the prior row's closing principal. Interest equals opening principal times the periodic rate. Principal reduction equals the total payment minus interest. Closing principal equals opening principal minus that reduction.

interest_t = opening balance_t × i
principal_t = payment - interest_t
closing balance_t = opening balance_t - principal_t

At a positive fixed rate with a level payment, interest generally declines and principal reduction generally rises. The first payment is not “mostly interest” by definition; the actual proportions depend on rate and term. In the Cedar Works 48-month example, a 0.5% monthly rate on $48,000 opening principal and a $1,127.281394… level payment produce $240 interest and $887.281394… principal in the first row.

The analytical schedule in this module uses full precision and should end within numerical tolerance of zero. Real servicers often round currency each period and adjust a final payment. Contract terms, fees, day counts, late payments, prepayments, variable rates, and disclosure rules can produce a different schedule. A classroom reconciliation is not a loan quote.

Accounting learners can use the schedule to understand principal-versus- interest evidence, but actual recognition, effective-interest accounting, classification, and disclosure require applicable guidance. Finance learners can use it to inspect cash-flow timing and total interest, but those amounts do not alone establish affordability or product suitability.