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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?

I thank you for your reply.

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;

add 1, giving 1.005;

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.

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for your reply.

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?

I thank you for your follow-up reply.

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%.

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