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QUESTION: Hello:

$0.60 represents interest on $600.00 at 6% for 6 days using a 360 day year. If the $0.60 is multiplied by, for example, 10, as in 10 days, the amount becomes $6.00, which represents interest on $600.00 at 6% for 60 days.

The calculation looks that the following: 10 X ($600.00 at 6% for 6 days) = 10 X $0.60 = $6.00.

Why are not the 6 days multiplied by 10 days also so that the number of days becomes 60 days? Only the interest of $0.60 is multiplied by 10. I would think that the calculation should be (10 days)/(10 days) X ($600.00 at 6% for 6 days) = (10 days)/(10 days) X ($0.60)/(6 days) = $6.00/60 days.

Why is 10 X ($600.00 at 6% for 6 days) = 10 X $0.60 = $6.00 sufficient?

I thank you for your reply.

ANSWER: You already are multiplying by 10 days. The 10 in the first equation is 10 days. The "days" unit was omitted, which is an error.

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

QUESTION: Hello:

I want to thank you for the reply.

Can you show me your idea of the correct calculation?

10 days X ($600.00 at 6% for 6 days)

How do the day units cancel in this calculation? The answer would be ($6.00 days) Would 6%/(360 days) be needed?

I thank you for your follow-up reply.

ANSWER: Hi Kenneth,

I am out of town and without access to MathType, so I cannot provide graphics showing the equations the way they would be written by hand. Not until I get back on my computer, that is.

Also, I misspoke when I said the units were omitted. There is indeed a missing unit, but it belongs in the denominator. The interest rate should be

6%/(360 days). The equation to calculate interest over 6 days would be

(600 dollars) * 6%/(360 days) * (6 days) = 0.60 dollar

The days units cancel out, leaving the answer in dollars.

To find the interest for 60 days, multiply by 10. The "days" unit applies to both the 6 and the 10. You do not multiply by another days unit because you are expressing the number of days, not square days (which do not exist). The commutative rule of multiplication allows you to change the order of the multiplicands, so the 6 and 10 can be combined to express the total number of days:

10*(6 days) = (10*6) days

The equation to calculate interest over 6 days can be used to calculate interest over 60 days:

10 *(600 dollars) * 6%/(360 days) * (6 days) = 10*(0.60 dollar)

which is equivalent to

(600 dollars) * 6%/(360 days) * (60 days) = 6.00 dollars

Again, the days units cancel out, leaving the answer in dollars.

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

QUESTION: Hello:

I want to thank you for your reply.

Does the following make sense?

Find the interest on $600.00 for 10 days @ 6%.

First, determine the interest one $600.00 for 6 days at 6%:

[$600 X (6%/360 days) X (6 days)] = $0.60 (The "day" units cancel.

= (10 days X [ $0.60])/6 days = $1.00 (Once again, the "day" units cancel leaving the dollar "$" units.

= (10 X $0.60) = $6.00 divided by 6 = $1.00

The complete calculation would appear as the following:

10 days X [$600 X (6%/360 days) X (6 days) X (6 days)]/6 days

----------------

And also, does it make sense to indicate the answer as $1.00 for 10 days since the "day" units have canceled?

I thank you for your follow-up reply!

I am not sure why you first calculated the interest on 6 days. Knowing the annual rate, you can calculate the 10-day interest directly.

600 dollars × 6%/(360 days) × 10 days = 1 dollar

If you need to calculate the interest for several different numbers of days, it is more convenient to calculate the rate of interest per day and just multiply that by the number of days.

600 dollars × 6%/(360 days) = 0.10 dollar/day

6 days × 0.10 dollar/day = 0.60 dollar

10 days × 0.10 dollar/day = 1 dollar

60 days × 0.10 dollar/day = 6 dollars

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