Question 111899: I am not sure how to set up and solve the formula for compound interest. I have the formula but not sure what goes where and the steps to solve this question.
Lee opened a retirement account with an initial investment of $10,000 at an annual interest rate of 8.5%. If the interest is compounded daily, how much will be in the account at the end of 25 years?
A=10,000 ?
P=?
r=8.5% ?
x=?
n=25 years ?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! This is a straight-forward compound interest problem. No matter what the numbers are, it works like this.
You are starting with $10,000 and the ANNUAL interest rate is 8.5%, but you are compounding daily. There are 365 days in a year (give or take) so at the end of the first day, you will have your initial investment plus one 365th of the annual interest. You can write it like this:  . The expression in the parentheses consists of 1 which gives you the amount of your initial investment plus the  which is the interest that you earned for that day.
At the end of the second day, you will have what you had at the end of the first day times that same expression again:
 , but you can also write this as:
 , the exponent being the number of days that have elapsed so far.
But you have a 25 year investment, so you need to know the number of days in 25 years, or 25 * 365 = 9125.
So, your complete expression is  . You need a REALLY good calculator, or use MS Excel. Just type the following into a cell on a blank Excel worksheet and you will get your answer: =10000*(1+(0.085/365))^9125
By the way, if you wanted to get really precise and use 365.25 as the number of days in a year, the answer comes out about $0.015 different. Or if you want to use the common financial institution practice of counting 360 days per year, the difference is about $0.29. In other words, don't sweat the small stuff.
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