It's only 2%

Quantitative Finance Level 2

A credit card charges a low monthly interest rate of 2%.

What is the effective APR?

27% 30% 24% 50% 2% 3%

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Calvin Lin by Calvin Lin

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2 solutions

Caleb Townsend
Feb 5, 2015

There are 12 months in a year, and the card charges 2% per month; therefore, the APR is 1.0 2 12 − 1 ≈ 0.27 1.02^{12} - 1 \approx \boxed{0.27}

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By the way, I noticed you have been posting a lot of financial questions lately. Will there perhaps be a "finance" category soon, alongside calculus, algebra, number theory, etc.?

Caleb Townsend - 6 years, 4 months ago

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perhaps! \quad

Calvin Lin Staff - 6 years, 4 months ago

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Is it an apr or apy ?Defining APR and APY  APR is the annual rate of interest without taking into account the compounding of interest within that year. Alternatively, APY does take into account the effects of intra-year compounding. This seemingly subtle difference can have important implications for investors and borrowers. Here is a look at the formulas for each method:

 For example, a credit card company might charge 1% interest each month; therefore, the APR would equal 12% (1% x 12 months = 12%). This differs from APY, which takes into account compound interest. The APY for a 1% rate of interest compounded monthly would be 12.68% [(1 + 0.01)^12 – 1= 12.68%] a year. If you only carry a balance on your credit card for one month's period you will be charged the equivalent yearly rate of 12%. However, if you carry that balance for the year, your effective interest rate becomes 12.68% as a result of compounding each month.

Ans for apr is 24% and apy is 27%

Arun Kumar Kundeti - 6 years, 4 months ago

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@Arun Kumar Kundeti – You are right in saying that the APR is 24%. However, the question asks for the effective APR , which is actually the APY, which is 27%. So yes, I was being slightly tricky there.

Can you add your comment about compound interest and the effects between APR and APY to the interest rate wiki? Thanks!

Calvin Lin Staff - 6 years, 4 months ago
Brock Brown
Feb 5, 2015

A quick snippet of Python will do the trick: 

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money = 1
for i in xrange(12):
    money *= 1.02
print "{0}%".format(100*(money-1))

This gives an output of 26.8241794563%.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Looks like I should come up with some coding questions for you :)

Do you know what a monte carlo simulation is?

Calvin Lin Staff - 6 years, 4 months ago

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I have some very vague idea of what it is, but I've never used it before. It looks pretty absurdly useful though. I'll check out what OpenCourseWare has to say about it.

And yes, PLEASE write some coding problems.

Brock Brown - 6 years, 4 months ago

I just wrote a problem involving Monte Carlo, is there any chance you can check its validity if you have the time?

https://brilliant.org/problems/erratic-systematic-wormhole-mathematics/?group=vx85tlq4qg1m&ref_id=606149

Brock Brown - 6 years, 4 months ago

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