An investment club placed $33,000 into two simple interest accounts. On one account, the annual simple interest rate is 6.5%. On the other, the annual simple interest rate is 4.5%. How much should be invested in each account so that both accounts earn the same annual interest?

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To find out how much should be invested in each account, we can set up an equation based on the given information.

Let's say the amount invested in the account with a 6.5% annual interest rate is x, and the amount invested in the account with a 4.5% annual interest rate is $33,000 - x (since the total investment is $33,000).

Now, let's calculate the interest earned by each account:
- The amount invested in the first account (x) will earn interest at a rate of 6.5%, so the interest earned will be 0.065x.
- The amount invested in the second account ($33,000 - x) will earn interest at a rate of 4.5%, so the interest earned will be 0.045($33,000 - x).

Since both accounts are earning the same annual interest, we can set up the following equation:
0.065x = 0.045($33,000 - x)

Now, let's solve this equation to find the value of x:

0.065x = 0.045($33,000 - x)
0.065x = 0.045($33,000) - 0.045x
0.065x = $1,485 - 0.045x
0.065x + 0.045x = $1,485
0.11x = $1,485
x = $1,485 / 0.11
x ≈ $13,500

Therefore, approximately $13,500 should be invested in the account with a 6.5% annual interest rate, and the remaining amount ($33,000 - $13,500) ≈ $19,500 should be invested in the account with a 4.5% annual interest rate.