Loan Amortization, explained.
Loan amortization is the repayment of principal through scheduled payments that also cover accruing interest.
Why it happens
A hypothetical 10,000-unit loan accrues monthly interest at annual rate divided by twelve. A level-payment formula determines the base payment; extra principal reduces later interest, and the last payment is capped.
Loan amortization is the repayment of principal through scheduled payments that also cover accruing interest.
Read the result
Compare remaining principal at the same month along both paths. A lower final interest total is not a lower selected monthly payment.
A worked example
Repay a fictional ten-thousand-unit loan
Use the initial fixed annual rate and term to inspect the base level monthly payment.
Add a fixed extra payment and compare the shortened schedule at identical calendar months.
Inspect the payoff month and total interest, keeping unrounded amounts and omitted fees separate from an actual contract.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A hypothetical 10,000-unit loan accrues monthly interest at annual rate divided by twelve. A level-payment formula determines the base payment; extra principal reduces later interest, and the last payment is capped.
Where this idea is useful
A practical use
Read a loan schedule to distinguish the payment amount, outstanding principal and total interest over its lifetime.
A common misconception
“Every equal monthly payment repays the same principal amount.”
Interest is charged on the changing balance first, so the principal component generally grows as outstanding principal falls.
What this explanation leaves out
- Teaching amounts are unrounded and omit fees, insurance, taxes, prepayment penalties and changing rates; actual contracts determine actual payments.
Why is the final payment smaller?
The model caps payment at remaining principal plus that month’s interest, preventing a negative final balance or an unnecessary overpayment.
Which portion of your payment actually reduces the balance on which future interest accrues?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.