Theory
APR: the real annual cost of a loan
APR vs interest rate: why "0%" can cost as much as a credit card, and how to compare loans by everything you pay, not by the advertised rate or the monthly payment.
~5 min read · 6 exercises · 250 points
Before you start
Zero percent, they said
Back with Sam's family, and this module is about debt. The credit card balance has grown and charges interest every month. Two ads offer to pay it off, and one promises 0% for 24 months, which sounds like the end of the problem.
In this first lesson you'll read the small print with Sam and learn to compare loans by everything you pay back, not by the advertised rate or the size of the monthly payment.
The price of a loan isn't the rate
The advertised interest rate is not the price. The price of a loan is simple to define: everything you pay back minus what you received — interest, fees, insurance, all of it.
Offer A is marketed as "0% interest", but it adds a monthly service fee of 1.9% of the original 52,800. Each month costs 52,800 / 24 = 2,200 of principal plus 0.019 × 52,800 = 1,003.20 of fee, so 3,203.20. Over 24 months that's 24 × 3,203.20 = 76,876.80 paid, and the price is 76,876.80 − 52,800 = 24,076.80 UAH — all of it fees.
Returning the 52,800 itself is not a cost; that money was never yours to keep. A "0%" headline describes only the interest line, not the price. Always total up what leaves your pocket and subtract what arrived in it.
- DoCost = 24 × 3,203.20 − 52,800 = 24,076.80 UAH.
- Don'tIt's 0% interest, so the loan is free.
The 1.9% monthly fee makes it cost 24,076.80 — nearly half the debt.
Compare by the real annual rate
To compare loans fairly, put them on one scale that already includes every fee: the real annual interest rate (called APR, or APRC in the EU, in English-language offers). Ukrainian lenders must disclose it, as of 2026, in ads and before you sign.
On that scale Sam's three options line up clearly: offer B costs about 37.1% a year, offer A about 46.8%, and the card 45.93%. So the "0%" offer is actually the dearest of the three, and B — a plain 32% with no fees — is the cheapest, saving about 4,700 over two years against A.
The traps to avoid: a 0% rate sitting next to a monthly fee tells you nothing on its own, and "3.2% a month" is not a small number once it's a year. One number, all-in and per year, is the only honest way to rank offers.
- DoRank by real annual rate: B 37.1% < card 45.93% < A 46.8%.
- Don'tPick A because the rate says 0%.
With its monthly fee, A is the most expensive of the three.
A monthly rate compounds
To turn a monthly rate into a yearly one, you can't just multiply by 12. Unpaid interest is itself charged interest the next month, so the rate compounds: the effective annual rate is (1 + r)¹² − 1, where r is the monthly rate.
Formula: P is the money you receive, A_t the payment in month t, r the monthly rate that makes the two sides equal, R the annual rate. Lenders follow a method set by the regulator; this is the idea behind it. · shown above
The card's 3.2% a month works out to (1 + 0.032)¹² − 1 = 1.4593 − 1 ≈ 45.93% a year. The simple sum, 12 × 3.2% = 38.4%, is noticeably lower because it pretends the interest never piles up on itself.
This is also why some figures look deceptively small. A US-style APR is often the simple version (monthly × 12), so it can read below the true compounded cost; the EU's APRC and Ukraine's real annual rate compound, like this formula. The higher the monthly rate, the wider the gap between the simple and compounded numbers.
- Do(1.032)¹² − 1 ≈ 45.93% a year.
- Don't3.2% × 12 = 38.4% a year.
Simple multiplication ignores compounding; the real figure is 45.93%.
A smaller payment can cost more
A smaller monthly payment is not the same as a cheaper loan. Often a lower payment just means a longer term, and a longer term at the same rate is more months of interest — a bigger total cost.
Sam's offer B is 32% over 24 months at 3,006.83 a month. The same 32% over 36 months drops the payment below 2,300, which feels lighter, but it stretches the interest over a year more, so the total paid is larger. The payment went down; the price went up.
So compare loans by total cost and the real annual rate, and use the monthly payment only for a different question: does it fit the budget this month? A loan can be both affordable per month and expensive overall — the two are separate checks, and only the all-in rate tells you which is truly cheaper.
What counts as the cost
The cost of a loan is everything you pay on top of the money you actually received. That includes the interest, every fee (a monthly service fee, a one-off issue fee) and any insurance that is a condition of getting the loan — if you can't get the loan without it, it is part of the price.
Two things are not the cost. The borrowed amount itself is returned, not paid: it was never yours to keep. And the price of what you buy with the money is a separate decision — the loan would cost the same whatever you spent it on.
The real annual rate is built to fold in all four cost items — interest and the three kinds of fee or required insurance — and leave out the two that aren't costs. That's why it, not the headline rate, is the number to compare.
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