# What is the effective APR? Vad är effektiv ränta?

Loans come in all shapes and sizes and it’s easy to lose sight on what’s a good deal and who is the wolf in sheep’s clothing. Do all these administration charges and dubious setup fees sound familiar? They might not look like much at first glance, but quickly grow to substantial sums and are only some of the ways greedy lenders hide behind seemingly attractive interest rates.

To counteract that we’ve got in the EU the standardized effective APR (Annual Percentage Rate of Charge) and the Standard European Consumer Credit Information form (known as SEKKI in Sweden) aiming to make loan offers comparable. But what is the effective APR actually and how is it calculated?

Well, technically it’s defined as this beauty:

If this makes you want to run away real fast I can assure you, you’re not the only one. So instead of getting stuck with the math let’s rather try to make general sense over what’s happening here.

At the core of it lies the principle that the monetary value of all payments you get (left side) should be equal to the monetary value of all payments you have to make to pay off the debt (right side) under normal circumstances. As most consumer loans are paid out directly and in full the equation becomes a little easier: the monetary value of all repayments need to be equal to the loan size.

Payments naturally include not only the nominal interest rate, but also all other fees (like administration, invoice or setup fees), so they’re all part of the effective APR as well. But it doesn’t quite end there. Let’s make an easy example:

• Loan size: 12 000 kr
• Repayment period: monthly over 12 equal instalments
• Nominal interest rate: 10%
• Monthly administration fee: 25 kr

Given these terms the monthly payment ends up at 1080 kr totalling 12 960 kr. That makes the finance cost tally up at 960 kr, which is 8% of the loan size. Now the effective APR is neither 10% nor 8% or even 12,5% (the value we get assuming the entire repayment is made at the end as a lump sum without any penalty), but rather ends up at 15,44%. How comes?

Turns out we’ve been missing one important aspect in finance, which is that money today is worth more than money tomorrow, be it due to inflation or growing uncertainties. That’s what interest rates generally are here for: compensation for affluent individuals to part from their money for some time. And that’s exactly the last ingredient we need to understand the effective APR: time.

The effective APR for consumer loans is the fictive interest rate under which the present value of all payments (i.e. discounted over time) is equal to the loan size.

What does that really mean practically for you? Well the absolute value not so much, but when compared across offers it’s a decent indicator for the true cost relative to each other.

Unfortunately it’s pretty tricky to calculate the actual figure as it requires an iterative approach to converge to the actual value, which is not precisely in the everydays repertoire of the average person. That’s why lenders need to disclose it easily accessible for loans under EUR 50,000.

Still, for all other cases it’s tricky to play around with the numbers. We’ve built an internal tool that helps us to visualize payment plans and are planning to publish it in the upcoming weeks if the interest is there.

UPDATE: we have published the calculator in the meanwhile, check it out!

Stay tuned!

Sven

Sven Perkmann