- #1
nickadams
- 182
- 0
Homework Statement
Write a script using a while loop that calculates the number of years it will take your bank account to accumulate at least $100,000 if you begin with s number of dollars, and you add that same amount at the end of each year. In addition, your account pays a percentage of interest, inter, every year.
Test your code for s = 500, inter = 5 and s = 1, inter = 50.
Homework Equations
In an attempt to find a general equation of money in the account as a function of years, I wrote the equation for the first 4 years and looked for a trend. The general form I found looks like...
$n = \frac{inter^n * s}{100^n} + 2*\frac{inter ^(n-1) * s}{100^ (n-1)} + \frac{inter ^(n-2) * s}{100^(n-2)} + \frac{inter^(n-3) * s}{100^(n-3)} + \frac{inter^(n-4) * s}{100^(n-4)}
... and it keeps adding these terms until the x in "inter^(n-x)" and "100^(n-x)" is equal to n. As you can see, when x is equal to n, the final term will be just an s. That is what we want because at the end of every year we add "s" to the account.
The Attempt at a Solution
How can I get that above equation in a general form so that I can use it in MATLAB to find dollars in the account as a function of years?
In order to solve the problem, I feel that I need to set up a while loop that will terminate once the dollars in the account exceed 100,000. But the problem is that I don't know how to put my function into MATLAB, and I also don't know how to identify how many years it took for the total $ to exceed 100,000.Please help!