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## 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 = [itex]\frac{inter^n * s}{100^n}[/itex] + 2*[itex]\frac{inter ^(n-1) * s}{100^ (n-1)}[/itex] + [itex]\frac{inter ^(n-2) * s}{100^(n-2)}[/itex] + [itex]\frac{inter^(n-3) * s}{100^(n-3)}[/itex] + [itex]\frac{inter^(n-4) * s}{100^(n-4)}[/itex]

... 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!