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# Word Problems/Simple Interest

Question
QUESTION: Hello:

Determine the simple interest for \$600.00 @ 10% for 60 days?

\$600.00 @ 10%/year = interest for one year

This amount is \$60.00. Using the banker's interest of 360 days for one year, the \$60.00 is multiplied by (60 days)/(360 days/year)
Since the days cancel out, how is the answer \$10.00 for 60 days?
Would it be more accurate to express the answer as \$10.00 for 1/6 year?

ANSWER: What you've done is correct.
As far as bankers go, 60 days and 1/6 years are both the same.

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

QUESTION: Hello:

I have a follow-up question.  I do not think you completely understood my question.

If the correct answer is \$10.00 for 60 days, how is it correct to include the 60 days as part of the answer since the days canceled each other out? Wouldn't the answer just be \$10.00?

I only put \$10.00 for 60 days to remind us how long the principal was held for.

To give a full description of interest problems:
P is the base amount, and that is \$600.00;
t is the time period, and that is 60 days, which is taken as 1/6 of a year;
i is the amount of interest, and that is 10%, which is 0.10 mathematically; and
I is the amount of money earned by interest, and that is \$10.00.

Each of these is a statement by itself.
When three of them are given, the 4th can be determined from the following equation:

For simple interest, the equation is I = inP where I is the amount of interest earned.
Here, i is the interest rate, n is the time period, and P is the principal amount.

For this problem, we had the following.  The value of I is \$60, for that was the amount earned.
The value of i is 10%, which in math is the same as 0.10, and that is the interest rate.
The value of n is 1/6, for n is the number of years.  The value of P is \$600, for that was the amount with which the problem started.

Hopefully this makes it clear what the variables in this equation are.

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

QUESTION: Hello:

Yes, I understand the simple equation of I = Prt, but I am more concerned with the so called "dimensional analysis" involved with the calculation. To my understanding the answer is just \$10.00. If someone indicates that it is \$10.00 for 60 day or per 60 days, then this is confusing because it could be correct, but it is also incorrect since the units of days canceled. Perhaps more accurate to indicate it as \$10.00 for 1/6 year. The unit "months" have canceled and the unit "year" remains, as "days" cancel in the following: (60 days)/(360 days/year).

I want to thank you for your help and assistance!

Note that, 'per' is the same as '/'.  That is, \$10 per 2 months is \$10 / (2 months).

As far as this problem goes, that is \$10/(2 months) or \$10/(60 days).
To convert \$10/(2 months) to the yearly interest, multiply by 12 months/year.
This gives (\$120/2) / year = \$60 / year.

The answer all depends on the wording of the question.

If they asked how much of an increase in funds there was, the answer is \$10.

If they asked how much was received over what time period, the answer would be \$10 in 2 months.

If they asked for the amount of interest that would be earned in one year at the current rate,

If they asked for the amount the funds increase by on the average, the answer could vary.
It is just like driving 90 miles in two hours.  It doesn't mean that there was 45 miles drive each hour, but that the average speed was 45 mph.  As far as the interest received, it could be said that on the average (over 2 month intervals), there be \$5 per month, \$10 per two months, \$15 per three months, \$30 per six months, \$60 per year, \$1 every 3 days, \$600 per decade,
50c every 36 hours, \$100 every ten months, or however else they decided to split it.
All of the answers in this paragraph are the same.

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

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#### Scott A Wilson

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