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QUESTION: Hello:

Why is an interest rate called a rate?  For example, a bank may offer a 6% rate on a loan.

A rate like 60 miles per hour or 60 miles/hour is a rate because there are two different units of measure in the rate "mile" and "hour".

What is the other unit of measure in 6% per ? or 6%/?. Is it the time [year] as in 6%/year?

ANSWER: If not otherwise mentioned, an interest rate of 6% refers to 6% per year.

Occasionally this refers to a one time payment,
as in if you pay \$200 at 6%, the interest would be \$12.

In almost every case, the interest is compounded monthly.

To get the effect interest rate, do the following:
convert to a number, so 6% is really 0.06;
divide by 12 (since there are 12 months), giving 0.06/12 = 0.005;
compute this to the 12th, giving 1.061677812; and
then subtract 1, giving 6.16778118644976%.

Most of the time, this is rounded to 6.1678% or 6.17%,
but I'm not sure if the banks round before or after computing the actual interest.

As an example, using N digits, I computed the interest on 1 million dollars.
If is is 2 places, the effective interest is 0.06 (or 6%), and the answer is \$60,000;
3 places gives 6.2%, and that is \$62,000;
4 gives \$61,700;
5 gives \$61,680;
6 gives \$61,678;
7 gives \$61,677.80; and
8 gives \$61,677.81.

More places accuracy results in the same as far as dollar value,
but fraction of a penny.

[an error occurred while processing this directive]---------- FOLLOW-UP ----------

QUESTION: Hello:

I am confused by  "...compute this to the 12th, giving 1.061677812; and
then subtract 1, giving 6.16778118644976%."

How did you get 1.061677812 and 6.16778118644976%?

What does "compute this to the 12th' indicate?

When we say something is raised to the 2nd, that means it is squared.
If I said 3 to the second power, that means multiply two 3's, as in 3*3.
The answer to this is 9.

If we say 3 is raised to the 5th power, that is the same as 3^5, and that means multiply
five 3's together.  In other words, take 3*3 * 3*3 * 3 = 9*9 * 3 = 81*3 = 243.

If we say 5 to the 6th power, that means multiply six 5's together.
That is 5*5 * 5*5 * 5*5.  We know 5*5 = 25, so that is 25*25*25.
Using a spreadsheet, it can be seen that 25*25 = 625, so 25*25*25 = 25*625.
Again, using the spreadsheet, 25*625 = 15,625.
From this, we can say that 5 to the 6th power is 5^6 = 15,625.

Now that we have an understanding of what powers are, let's get back to interest.

When the bank today says 12% per year, they really mean 1% per month.
When we say 1% per month, that means each month the amount is multiplied by 1.01.
To get the effect rate, multiply 1.01 by itself 12 times, and this is 1.01^12.
That turns out to be 1.12682503013197.

The one in front is what it takes to leave the amount the same, so the interest rate is the amount above 1.  Subtract 1 from 1.12682503013197 and get the interest rate of
0.126825..., which is just put as 0.1268 or 12.68%.

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the reply and clarification!

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#### Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.