APR versus Interest Rate

A loan advertisement can show two percents that both look like “the rate.” One is the interest rate used to charge interest on the balance. The other is a comparison figure — APR in the US and UK consumer-credit vocabulary, TAEG in much of the EU — built so that fees and the interest together have a single percent attached. They coincide when there are no fees and the day-count conventions line up. They separate as soon as someone charges an arrangement fee, a mandatory insurance premium, or a discount that is really a fee in disguise.

PercentBox’s loan calculator uses the nominal rate you type to build a fixed installment and an amortization schedule. It does not compute a regulated APR. This page is about not feeding it the wrong one of the two numbers, and about not treating either number as the full cost in euros.

What the installment actually uses

The EMI formula wants a monthly rate. Lenders usually take a nominal annual rate and divide by 12. That nominal rate is the one that reproduces the payment. If the contract says 6.5% and the payment matches the formula at 6.5%, you have found the nominal rate. The walk-through of that formula, including a €25,000 example, is in how loan EMI works.

If you instead type a higher APR that was inflated by a €400 fee, the calculator will invent a higher payment than the lender will collect each month. You will think the offer is less affordable than it is, month to month, and you will still need to remember the €400 leaves your account up front. The fee and the installment are both real. They are not the same cash flow, so they do not belong in the same input box unless the tool was built to model both.

What comparison rates are trying to do

Suppose two 5-year loans of €10,000.

• Lender A: 7% nominal, no fees. Payment about €198 a month. Total paid about €11,880. Cost of credit about €1,880.
• Lender B: 6.4% nominal, €300 arrangement fee taken at the start. Payment about €195 a month. Total of payments about €11,700, plus the €300, so about €12,000. Cost of credit about €2,000, and you did not even receive the full €10,000 to spend if the fee was deducted from the advance.

B’s monthly payment looks cheaper. B costs more once the fee is included, and the amount of cash you actually received may be smaller. A regulated APR/TAEG is an attempt to put A and B on one percent scale so the fee cannot hide. The exact percent depends on the legal recipe (which fees count, how the time value is calculated). I am not going to pretend a two-line formula reproduces your country’s APR. I am going to say: if B’s comparison rate is higher than A’s, believe that ranking over the ranking of the nominal rates, then still look at the euro totals.

A sketch you can compute without claiming it is “the” APR

One rough classroom approach treats the fee as reducing the net advance, then asks what rate would make the payment you will actually make consistent with that smaller advance. That internal rate is in the spirit of a comparison rate. It will not match a legal APR to the decimal, because the legal one has rules about which charges are finance charges and about day count. Use it as intuition: fees raise the true rate above the nominal, more so on short loans and small principals, because a €300 fee is a large fraction of a €2,000 one-year loan and a smaller fraction of a €200,000 mortgage.

On short loans, compare euros of interest plus euros of fees. On long loans, a small rate gap compounds into a large euro gap, so the nominal rate regains importance and the fee matters less relatively — unless the fee is itself a percent of the loan. A 2% arrangement fee on €200,000 is €4,000. That is not a rounding error. Put it in the cash column even when the APR difference looks like a few tenths of a point.

Nominal, effective, APR

These three get stacked in casual speech.

• Nominal annual rate: the contract rate before you worry about monthly compounding or fees. Often divided by 12 for the payment.
• Effective annual rate: what a year of compounding does to a balance with no fees, from the EAR formula. Monthly compounding makes the effective rate a bit higher than the nominal.
• APR / TAEG: a regulated comparison price of the credit, which may include fees and may be defined so that it is comparable across lenders. It is not “nominal times something” you should invent.

A savings APY and a loan APR are both “one percent that already did some combining,” and they are not interchangeable. Do not subtract a savings APY from a loan APR and call the difference your spread without reading what each percent includes.

Variable rates

If the nominal rate is Euribor plus a spread, both the payment and any APR illustration that assumed a constant index will go stale when Euribor moves. The comparison rate in a pre-contractual sheet is tied to the assumptions printed on that sheet. When the index changes, rerun the payment at the new all-in nominal rate. Do not add the index change to the APR as if both were percentage points of the same object unless the disclosure tells you to. Percentage points are the right unit for “the index rose by 0.5 points.” The effect on APR is a second calculation.

When to use the loan calculator

Use it with the nominal rate to see the installment, the total interest, and the shape of amortization. Then add fees that the calculator omitted, in euros, on the side. Compare two offers on total euros paid and on cash received today, not only on the lower monthly payment.

Use a published APR or TAEG as a ranking signal produced under a known legal definition, and read which fees it claimed to include. If the APR is high and the nominal rate is low, hunt the fee. If you cannot find a fee and the two percents still disagree, you may be looking at a compounding or day-count difference, and the lender’s repayment schedule — not a generic calculator — is the document that wins.