Sophie borrowed $2000 and took 3 years to repay the loan and $900 interest. What was the per annum simple interest rate?

900x3
=2700-2000
= 700 is the amount he payed more than lone

I = p * r * n

i is the interest
p is the principal
r is the interest rate per time period
n is the number of time periods.

in your problem:

i = 900
p = 2000
r = what you want to find
n = 3 years

formula becomes 900 = 2000 * r * 3

solve for r to get r = 900 / 2000 / 3 = .15

that's .15 interest rate per year = 15% per year.

at a nominal interest rate of .15 per year, the interest rate per month would be .15/12 = .0125 per month.

the remaining balance at the end of 6 month is equal to 1907.140183