Expert: Sherry Wallin - 6/14/2009

Question
QUESTION: Hello:

How is the following solution found for the following:
(100^365/73)/5 or if typed as follows in which this version my be easier to understand.

100^365/73
----
73

I thank you for your reply.

ANSWER: Hi Kenneth~
    The two are NOT equivalent...what is equivalent to the first is:
(100^365/(73*5)). Taking 100 to the 365th power just adds 365 zeros to 100. Meaning that there are 367 zeros. If you divide by 73*5 = 375, then you will get whatever 1000/365 is and 3 less zeros (364 zeros).

Math Prof

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

QUESTION: I want to thank you for the for reply.

I have added an attachment (I hope you can open it) with this follow-up question.
How is it solved? I do not know what to do with the fractional exponent.

The exponent in the calculation has two symbols. The # represents number of days in the year and the black square box represents umber of days since the account was opened or started.

I thank you for the reply.

ANSWER: Kenneth~
    There are a couple of ways to interpret a fractional exponent. The denominator is the root and the numerator is the power. With that said, in this problem you would do open parenthesis, Current account Value divided by starting account value, close parenthesis then use the y^x key on your calculator and enter the fraction in parentheses. Total that and then subtract 1 from the total. If I haven't answered your question try me again :)

Math Prof

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QUESTION: Hello Math Prof:

I want to thank you for the reply.  Can you provide an example? Just make up some amounts that can be used in the calculation that I sent to you and explain what to do.

I thank you for your willingness to help.

Answer
Hi Kenneth~
    The # sign represents the number of days in the year because there are not 365 days in each year because of leap year. So most of the time this number will be 365 except for leap year. That fractional exponent is looking at the ratio of number of days in a year to the number of days since the account opened. When you've had the account longer than 1 year = 365 days then that ratio will be less than 1. Are you sure you have those symbols described correctly and in the correct spot? It makes more sense to me that you'd want that ratio to get bigger than 1 the longer you have the money in there. But, that is just off the cuff, a hunch but worth having you check out. Using the values the way you stated then suppose you started with nine hundred dollars and the current value was 1000 and you've had the account opened for 6 months = 183 days. Then you would have (1000/900)^(365/183) - 1 =  .233857315. This only makes sense if you have put the money in an account like an annuity and it has a surrender value that exceeds it's original value. How do I know this? What is in the parentheses is greater than one raised to a power that is greater than one so your number (1000/900)^(365/183) will be bigger than 1 so that when you take 1 away from it you will have a positive number. Unless you are suppose to multiply this .233857315 times the investment and in that case you would have $210.47. Again I don't know what formula you are using or if it is correct but this is what happens with the formula you gave me.

Math Prof