Expert: Sherry Wallin - 6/15/2009

Question
Hello Math Prof:

I want to thank you for your reply.

I need to send this follow-up question to the one below because I reached the limit.

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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.

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Here is your question from above: "Are you sure you have those symbols described correctly and in the correct spot?"

I sent you the equation as an attachment. I suppose that it is correct. I did not make any changes to it. It is used to determine the annual percentage return. That's all I know.  

Answer
Hi Kenneth, I didn't put in those number(#) symbols in my calculation above FYI. Hmmm...as I said above the exponent is greater than 1 when you've had the money invested less than a year which makes the value bigger and when you've had the money invested more than a year then the exponent is less than 1 which will make the return smaller. By the way the square root of a number is a number to the 1/2 power. 1/2 is certainly less than 1 and take any number and take it's square root and find out that it is smaller. One last thought in that formula you gave me it has in the denominator your initial investment and in the numerator the current value. I'm not sure how the current value is determined but the ratio between the current value and the initial investment should be at least one so you have number greater than 1 in the parentheses. It is possible that this is a valid formula but the exponent still bothers me...

Math Prof