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QUESTION: Hello:

The simple interest calculation is as follows:

P X R X T = interest

Here is an example:

$600 X 6% X 60/360. I am using 360 days as the days in a year for this calculation.

Now the 6% is the annual rate; so I assume that it can be expressed as 6%/year.

So, now the calculation appears as $600 X 6%/year X time.

The time is expressed as 60 days or 60/360. I believe that 60/360 represents a fractional part of one year; so the calculation is now $600. X 6%/year X (60/360) year. I think that this is correct, but I'm not totally sure. The "years" cancel from the calculation.

The calculation, I think, can use days instead of years.

$600 X 6%/(360 days) X 60 days = $6.00 The "days" cancel from the calculation.

I think the following calculation is not correct: $600 X 6%/(360 days) X 60/360 year. There are two "360" that will prevent the calculation from providing the correct answer.

So, my question is as follows: Are 1. and 2. below correct and is 3. incorrect?

1. $600 X 6%/year X (60/360) year = $6.00

2. $600 X 6%/(360 days) X 60 day = $6.00

3. $600 X 6%/(360 days) X 60/360 year = $0.016666...

I thank you for your reply.

ANSWER: #s 1. and 2. are correct.

The way I think of this is, given the principal P = $600, R = annual interest rate and T = time after the principal starts compounding (T = 0, i.e, right away), then

Interest = P･R･(fraction of year).

It looks like fraction of year you are interested in is 60 days/360 days = 0.167, so

I = P･R･(60/360).

As your solutions 1. and 2. indicate, you can use the fraction of the year that the interest rate has been working on the principal (#1) or the fraction of the interest rate R that corresponds to 60 days, R/360 (#2). I prefer the 1st way, but whatever.

Let me know if this makes sense.

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

QUESTION: Hello:

I want to thank you for your reply!

Yes, your reply makes sense to me. I do have one other calculation that I do not understand why it is incorrect. It is similar to my 2. calculation.

$600 X 6%/(360 days/year) X 60 days = the "years" need to cancel or the answer is 6.00 dollar years or $6.00 years, if I'm not mistaken. This calculation is incorrect, but I do not know why.

I used years in 360 because there are 360 days in a so called banker's year.

I thank you for your follow-up reply.

I'm not sure why you say the calculation is incorrect. Did you take into account that 6% really means the fraction 0.06? Also, just to be a little more rigorous (and to make sure we are on the same page), you should precisely define the terms and variables you are using. Eg., T = a fraction, with no units, not years or days or any other unit of time. Are you being consistent with your units?

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