The question states: $\$500$ deposited @ time $= 0$, and then $\$1000$ deposited @ time $=3$ for a total of $12$ years. I need to find the value @ time = $12$. Discount rate = $7.5\% $
So, my equation is -> $$500\times (1.075)^{12}+1000\times (1.075)^9 = \$3108.128$$
In this case the expected answer is: $\$3291.38$ What am I going wrong ?
UPDATE: I figured it out.
$$500\times 1/(1-0.075)^{12}+1000\times 1/(1-0.075)^9 = \$3291.38$$
I write some details, which explains why your equation is right. The discount factor is
$$\frac{1}{1+i}=1-d,$$
where $d$ is the discount rate and $i$ is the interest rate. Keep that relation in mind. Now you want to compound the payments. For this purpose you take the reciprocal.
$$1+i=\frac1{1-d}=\frac1{1-0.075}=\frac1{0.925}$$
This is the factor for compounding. I hope it clarifies some things.