Calculting interest on investment Given an investment of 9550000 USD I want to know what the value of this investment is after one year if I have to pay 10% of interest per year. 
According to my understanding, that would be 90% of the investment which equals to 8595000 USD.
According to the solutions, however, it is  8681818 USD.
I can see that this is around 91% of the initial investment. Which formula for the calculation of interests, however, is used to arrive at this?

You need to phrase your question carefully.  It looks like you are looking for the amount you would have to invest today to have $9550000$ in one year if the interest rate is $10\%$, which is not what you asked.  If $P$ is the principal you invest today, after one year you have $1.1P$.  We want 
$$1.1P=9550000\\P=\frac{9550000}{1.1}=8681818$$
Note that dividing by $1.1$ is not the same as multiplying by $0.9$
