4
$\begingroup$

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.

1 Answers 1

6

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:

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

  • 1
    @And$r$é: The com$p$anies 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.2011-07-22