The interest they call zero

Challenge of the day #63A new one every day at midnight UTC

Today's offer

The price is 7700 in cash, or 8 instalments of 1110.84 with no interest. What monthly rate is hidden in that? Answer as a percentage.

Type your answer with two decimals. Within one per cent counts as close, and the arrow points from your answer to the right one.

Your answerHow close

Yesterday's answer1.70

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How can an offer with no interest have a rate?

Because the cash price is lower. Paying over time means giving up that discount, and the difference between the two has an exact monthly rate hidden in it. The shop is not lying about the instalments; the interest is in the price you did not take.

Find the monthly rate that makes all the instalments, brought to today, add up to the cash price. That rate is the answer.

Why is the rate not simply the total divided by the price?

Because the instalments are paid at different times, and money at different times is not the same money. Dividing the total by the cash price ignores that you keep most of the amount for months, which is exactly what makes the real rate lower than that quick division suggests.

Which rate is the right answer, exactly?

The one that comes out of the three numbers on the screen. The generator rounds the instalment to cents before showing it, and rounding moves the rate in the third decimal, so the answer is recomputed from what you can see. Otherwise a correct calculation would be marked wrong.

Is this advice about paying cash or in instalments?

No. It is an exact calculation on three numbers, with no product, no shop and no recommendation. What you do with the number is yours.

Can I use a calculator?

Yes. This is a problem to solve, not a memory test. The site has calculators for instalment plans, and using them is the point of having them.

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