Math help? (Finance)

You’ve got the wording all backwards. This should be obvious if you knew what the words meant, as “accumulate to” means the final amount after interest is added, so it would need to be that amount should be more than the invested amount.

A $9000 deposit made today will accumulate to $10,129.58 after two years at 6% compounded semi-annually, not vice versa!

The way you would calculate it brute force would be to add interest to the total balance after each period, which happens every 6 months, so twice a year, so it would happen 4 times in two years.

So you’d take the balance invested, and multiply that by 1.06 to get the interest.
Then you’d add that interest to the balance. That’d be the balance in six months.

Then you’d take THAT balance and do the same multiplication to get the interest in the next period, and add that interest to that balance, to get the amount after one year.

Then you’d do that same thing two more times to get the balance after two years.

I think that must be the question they’re asking you. If they’re asking you the reverse of that problem, then they must think you have a much greater understanding than you seem to, so in that case I’d tell you to go talk to your teacher. But I don’t think the question can really be what you wrote for students at the level that would ask this question.

I agree with @Zaku that you seem to have gotten things backwards. The question appears to be, how much money will you accumulate on a $9000 deposit after two years at 6% interest compounded semi-annually?

Semi-annual interest means 3% interest per half year, giving you a factor of 1.03 for principal plus interest. In 2 years there will be 4 semi-annual periods, so that the total in the account will be (1.03)^4 x $9000, which rounds to $10129.58

As for the original question, to get how much you would have to deposit to get $9000 in two years, that would obviously have to be less than $9000. This is the reverse of what was done for the previous answer. In this case we divide by (1.03)^{4 instead of multiplying, giving $9000/(1.03)}4 = $7996.38.