You are trying to determine how much interest you will make over N years when you are making X percentage each year.

So you invest 10,000 for N years

10k * N = 10,000N

Percentage is calculated by X/100

So in this case $10,000N(x/100) = interest made over N years

If its easier for you to see, plug in some default values for N and X

so why not this solution? why am i wrong?

10,000 * [1+ (x/100)]^n - 10,000

The key term is SIMPLE INTEREST RATE. The growth is only based on orignal investment. You are thinking about the problem as compound interest growth such as a 401k which in this case it is not.

Simple Interest = p * i * n
p = principal (original amount borrowed or loaned)
i = interest rate for one period
n = number of periods

Translate the question in these term. You invest $10 for 5 years, what is the total interest made if you make 10% interest on the initial investment amount each year.

10*5(.10) = $5 over 5 years You make $1 per year.

Now i see. Thanks.