Workspace
The calculator's own fields, action and results arrive with the verified pack when you load it. Nothing is computed in this page.
Loan comparison · two offers priced together
Compare two loans by payment, interest and total cost
Price two fixed-rate loans side by side and read the difference in monthly payment, total interest and lifetime cost, each computed by the engine rather than by eye.
Verified engine
What the engine returns
The monthly difference comes out negative — the first offer’s instalment is the smaller of the two. The lifetime-cost difference comes out positive — the second offer costs less over its full term, despite its higher rate, because its payments stop years sooner. And with equal principals the interest difference matches the total-cost difference exactly. The same instrument on two identical offers returns a difference of zero in every measure, which is a useful sanity check.
Inputs the result is built from
First loan principal
First loan annual rate
First loan term
Second loan principal
Second loan annual rate
Second loan term
How the result is derived
MethodThe annuity payment closed form prices each leg from its principal, monthly rate and payment count; totals and interest follow per leg, and the monthly, interest and total-cost differences are subtracted inside the engine, first leg minus second.
StandardLevel-payment amortisation applied to two loans with engine-computed differences
GuardEach principal must be positive: a leg with nothing borrowed has no instalment to compare, and the calculation refuses rather than pricing an empty loan.
Why the monthly winner and the lifetime winner differ
Each leg is priced independently: the annual rate becomes a monthly rate, the term in years becomes a count of monthly payments, and the level instalment follows from the annuity relation — with a zero rate handled as its own case, where the instalment is simply the principal spread evenly across the payments.
From each instalment come the totals: the instalment times the payment count is everything paid over the life of the loan, and that total minus the principal is the interest. The differences are then taken inside the calculation — the first leg minus the second, in each measure — so a positive lifetime-cost difference means the second offer is the cheaper one over its full term.
The measures genuinely disagree. An offer with a longer term and a lower rate can carry the smaller instalment while costing far more over its life, because the smaller payment is collected many more times. Which difference matters is a question about your constraint — a tight month favours the instalment, a long horizon favours the lifetime figure.
When the two principals are equal, the interest difference and the total-cost difference collapse into the same number, since the borrowed amounts cancel. When the principals differ — say one offer rolls fees into the borrowing — the two differences separate, and the gap between them is itself informative.
The annuity payment closed form prices each leg from its principal, monthly rate and payment count; totals and interest follow per leg, and the monthly, interest and total-cost differences are subtracted inside the engine, first leg minus second.
When this calculation is used
- Holding two genuine quotes against each other before accepting either.
- Testing whether a shorter term at a higher rate beats a longer term at a lower one — the classic case where the measures split.
- Seeing what rolling fees into one offer’s principal does to its lifetime cost.
- Reducing a refinance decision to the same three differences before a fuller closing-cost analysis.
Worked example
Two offers on the same principal: the first at a slightly lower rate over a long term, the second at a slightly higher rate over a markedly shorter one.
The monthly difference comes out negative — the first offer’s instalment is the smaller of the two. The lifetime-cost difference comes out positive — the second offer costs less over its full term, despite its higher rate, because its payments stop years sooner. And with equal principals the interest difference matches the total-cost difference exactly. The same instrument on two identical offers returns a difference of zero in every measure, which is a useful sanity check.
Every figure on the page is produced by the certified engine at load time, and the release it comes from is checked against the test vectors the signed pack itself declares — nothing here is worked by hand and nothing is stored in the prose.
What each input represents
First loan principal
The amount borrowed under the first offer. Fees financed into the borrowing belong here; fees paid at the table do not. It must be positive for the leg to be priced.
First loan annual rate
The first offer’s nominal annual rate as a percentage. It is divided down to a monthly rate before use, and a zero rate is legitimate — it prices as an interest-free schedule.
First loan term
How long the first loan runs, in years. It is converted to a whole count of monthly payments, and it must be positive.
Second loan principal
The amount borrowed under the second offer, treated exactly as the first. Entering different principals is allowed and is how financed fees show up in the comparison.
Second loan annual rate
The second offer’s nominal annual rate as a percentage, converted to a monthly rate the same way — the two legs always share one convention.
Second loan term
The second loan’s term in years, converted to its own monthly payment count. Differing terms are the usual reason the monthly and lifetime verdicts disagree.
Assumptions and limits
- Both loans are fixed-rate, fully amortising, with level monthly instalments and no balloon.
- The monthly rate is the annual rate divided by the months in a year — a nominal quoting convention, not an effective annual rate.
- Neither leg includes fees, points, insurance or taxes unless you fold them into that leg’s principal yourself.
- The differences are always the first leg minus the second, so their signs read consistently: positive means the second offer is the smaller number.
- This is an educational reference, not financial advice — a lender’s full disclosure and your own circumstances decide the choice.
What the guards protect against
- Each principal must be positive: a leg with nothing borrowed has no instalment to compare, and the calculation refuses rather than pricing an empty loan.
- Each term must be positive, so that every leg has a real payment count to amortise over.
- The refusal is deliberate output — when either leg cannot be priced, no difference is reported at all, because half a comparison is worse than none.
Provenance
Level-payment amortisation applied to two loans with engine-computed differences
The annuity payment closed form prices each leg from its principal, monthly rate and payment count; totals and interest follow per leg, and the monthly, interest and total-cost differences are subtracted inside the engine, first leg minus second.
Educational reference, not financial advice, and not an APR comparison — fees and disclosures sit outside it. The signed pack carries its own citation; the page reports the verification state of the release it mounted rather than asserting one.