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If my current credit card balance in July is \$1,000 USD, my credit card's APY is 20% and this month I made a payment for \$100 on time (to avoid late fees)... What will my balance be in August?

I don't think it will be \$900 or \$900 + 20%. It should be $900 + some amount I don't know how to calculate.

I kind of remember this involving compound interest and/or logarithms, but I honestly don't remember most of my math classes beyond pre-cal. Could someone point me in the right direction?

Thanks.

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1 Answer 1

up vote 6 down vote accepted

There are some potential wrinkles about compounding and about how exactly to divide up the APY, but essentially, the APY is the annual percentage, so per year. For each month, you're probably paying $\frac{1}{12}$ of that, or possibly $\frac{30}{365}$ or $\frac{31}{365}$ os some other strange computation for a portion of that rate.

Supposing it's $\frac{1}{12}$, $\frac{1}{12}$ of $20\%$ is $\frac{1}{12}\cdot20\%=\frac{5}{3}\%=1.66666...\%=\frac{5}{300}$, so your balance is probably going to be something like $$\$900+\frac{5}{3}\%\cdot\$900=\$900\cdot(1+\frac{5}{300})=\$915.$$

This assumes no new purchases, no other fees, etc.

edit: Actually, it's more likely that if your balance was $\$1000$ and you paid $\$100$ on time, they charged you interest on the balance of $\$1000$, then subtracted your payment, to get your new balance:

$$\$1000+\frac{5}{3}\%\cdot\$1000-\$100=\$1000\cdot(1+\frac{5}{300})-\$100\approx\$916.67.$$

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1  
If they are supposed to reveal effective interest rate, which I think they are in the US, the calculation would be different. –  André Nicolas Jul 22 '11 at 3:09
    
@Isaac: Very clear answer, thank you! –  Christian Correa Jul 22 '11 at 3:27
    
@André Nicolas: What is effective interest rate and how different would the calculation be? I am in the US so what you're saying probably applies to my credit card. –  Christian Correa Jul 22 '11 at 3:28
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@Isaac: I think they have to reveal effective APR, which is not the same as nominal APR. Usually compounding is daily, but on average daily balance during the month. It is very messy mathematically. Your answer is larger but not much larger than the actual number they compute. A twist: if you borrow $100$ on your credit card, all that you owe becomes subject to interest, without the usual grace period! Details differ. Get a pair of magnifying glasses and read the details of the agreement you signed, unless you threw it away. –  André Nicolas Jul 22 '11 at 3:45
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@André: The companies most definitely have to reveal both the underlying rate and the effective rate. Usually, the one that's a "pretty" number, like 19.99% is the rate and the one that's 21.927% is the effective rate. Regardless, whatever one computes by hand is likely to be an approximation at best, due to the intricacies of what things are subject to what interest, compounded how, and starting from when, according to the agreement, which they almost certainly also have to send you a copy, should you request it. –  Isaac Jul 22 '11 at 3:48

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