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What is the difference between APR and APY? And which one is best?
Posted 27th June 2014 at 05:14 PM by David Beroff
Tags apr, apy, compounding, growth, yield
Annual Percentage Rate (APR) and Annual Percentage Yield (APY) are standardized ways of describing the amount of money that you might pay on a loan or earn on an investment, but what do they really mean, and what is the difference between the two phrases? Even more importantly, how can you use these numbers to determine what is the best opportunity for you?
The APR is the amount that an investment (or loan) grows in a given period, multiplied by the number of those periods in a year. The growth is expressed as a percentage, relative to the balance before the growth. Rather than using simple multiplication, APY takes compounding into effect; it expresses how an investment or loan can or will grow over a one year period.
To calculate Annual Percentage Rate (APR), simply multiply a period's rate of growth for each period by the number of periods in a year. So if your investment pays interest semiannually, (twice a year), just multiply the rate by two. Monthly payments would multiply each month's growth rate by 12 to get the APR.
(Video source: "Fidelity Fiduciary Bank", Mary Poppins (1964), Disney)
When you calculate Annual Percentage Yield (APY), you need to account for the compounding of the investment or loan, which is why the formula uses exponentiation. Take the sum of one plus the period's growth, and then take that to the power of the number of periods in a year, finally subtracting one at the end to get the APY.
Put a different way, APR is a good way to determine how much you will get paid (or will pay) in a specific month; just divide the APR by twelve. On the other hand, APY is a good way to see how a fund can grow (with compounding) over an entire year.
For example, in my earlier blog entry, I mentioned that our investment club pays every member around 2% per month. Let's take a hypothetical investment of $1,000 that earned exactly 2% per month to see how the numbers would work.
Each month sees a growth of 2%, so to get the Annual Percentage Rate (APR), just take 2% times 12 and you get 24% APR.
You can also see the effect of compounding, where each month's interest is slightly more than that of the prior month. To get the Annual Percentage Yield (APY), you'd take the sum of 1 plus 2% (2/100), or 1.02, and multiply it by itself (1.02 * 1.02 * 1.02 ...) a total of twelve times. That's what exponentiation does, so you can simply take 1.02 to the 12th power and get 1.268. Once you subtract the one, you're left with 0.268, or 26.8/100, which gives you an APY of 26.8%.
Also notice how you can see that same 26.8 figure when you observe how the $1,000 grows to $1,268.24 after one year.
One might ask, "Which number is better?", but the question does not really make sense, since APR and APY describe different things. Companies which offer loans almost always stress their APR, since this number is lower, and they know you want to choose the lowest rate among competitors. Similarly, companies looking for your investment will stress their APY, since this number is higher, and you generally want to maximize the amount of return (i.e., yield) on your money.
With any investment, you should always see how a company has been doing, but make sure that you realize that past performance is never a guarantee of future returns.
To summarize, many loans and investments compound monthly, and the amount that the balance changes each month is a twelfth of the APR. The APY, on the other hand, shows how a given vehicle (a loan or investment) performs when that growth is extrapolated out to one year, with compounding, on a standardized basis.
If you have any questions, please message me, or simply email me: David (at) Beroff (dot) com.
_____
Full disclosure: Yes, of course I earn referral income when you join.
And you'll be able to do so, as well. :-) Past performance is never a
guarantee of future returns. Only invest what you can afford to lose.
The APR is the amount that an investment (or loan) grows in a given period, multiplied by the number of those periods in a year. The growth is expressed as a percentage, relative to the balance before the growth. Rather than using simple multiplication, APY takes compounding into effect; it expresses how an investment or loan can or will grow over a one year period.
To calculate Annual Percentage Rate (APR), simply multiply a period's rate of growth for each period by the number of periods in a year. So if your investment pays interest semiannually, (twice a year), just multiply the rate by two. Monthly payments would multiply each month's growth rate by 12 to get the APR.
(Video source: "Fidelity Fiduciary Bank", Mary Poppins (1964), Disney)
When you calculate Annual Percentage Yield (APY), you need to account for the compounding of the investment or loan, which is why the formula uses exponentiation. Take the sum of one plus the period's growth, and then take that to the power of the number of periods in a year, finally subtracting one at the end to get the APY.
Put a different way, APR is a good way to determine how much you will get paid (or will pay) in a specific month; just divide the APR by twelve. On the other hand, APY is a good way to see how a fund can grow (with compounding) over an entire year.
For example, in my earlier blog entry, I mentioned that our investment club pays every member around 2% per month. Let's take a hypothetical investment of $1,000 that earned exactly 2% per month to see how the numbers would work.
Each month sees a growth of 2%, so to get the Annual Percentage Rate (APR), just take 2% times 12 and you get 24% APR.
You can also see the effect of compounding, where each month's interest is slightly more than that of the prior month. To get the Annual Percentage Yield (APY), you'd take the sum of 1 plus 2% (2/100), or 1.02, and multiply it by itself (1.02 * 1.02 * 1.02 ...) a total of twelve times. That's what exponentiation does, so you can simply take 1.02 to the 12th power and get 1.268. Once you subtract the one, you're left with 0.268, or 26.8/100, which gives you an APY of 26.8%.
Also notice how you can see that same 26.8 figure when you observe how the $1,000 grows to $1,268.24 after one year.
One might ask, "Which number is better?", but the question does not really make sense, since APR and APY describe different things. Companies which offer loans almost always stress their APR, since this number is lower, and they know you want to choose the lowest rate among competitors. Similarly, companies looking for your investment will stress their APY, since this number is higher, and you generally want to maximize the amount of return (i.e., yield) on your money.
With any investment, you should always see how a company has been doing, but make sure that you realize that past performance is never a guarantee of future returns.
To summarize, many loans and investments compound monthly, and the amount that the balance changes each month is a twelfth of the APR. The APY, on the other hand, shows how a given vehicle (a loan or investment) performs when that growth is extrapolated out to one year, with compounding, on a standardized basis.
If you have any questions, please message me, or simply email me: David (at) Beroff (dot) com.
_____
Full disclosure: Yes, of course I earn referral income when you join.
And you'll be able to do so, as well. :-) Past performance is never a
guarantee of future returns. Only invest what you can afford to lose.
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