Because the rate is annual (8% and 9%), and our timeline for investment is 1 year, the math is fairly simple.
We have ten thousand to invest, so we can use one variable to express the amount we will invest in each account: Account 1 = x Then, after putting x in the first account, the rest of the money, or (10,000-x) will go into account 2.
Now, because it is just one year, calculating the amount of interest earned on a given account can be done by multiplying the amount of money in the account by the annual interest rate:
0.08*(account one) + 0.09*(account two) = total interest earned
In other words:
0.08*(x) + 0.09*(10,000-x) = 860.00
From there, it is just doing the math out to find x (account 1)
0.08x + 900 - 0.09x = 860
-0.01x = -40
x = 4,000 (aka. Account 1 = 4,000)
Therefore, account two = 10,000 - 4,000 = 6,000
A1 = 4,000
A2 = 6,000