Final answer:
To evaluate the expression $500(1+0.045)^2 -$500(1+0.04)^3, we can use the exponentiation rule and substitute the given values. The result is $32.44.
Step-by-step explanation:
In this question, we are asked to evaluate the expression $500(1+0.045)^2 -$500(1+0.04)^3.
To solve this, we can use the exponentiation rule that states (a+b)^n = a^n + na^(n-1)b + n(n-1)/2!a^(n-2)b^2 + ... + nb^(n-1).
Substituting the values into the formula, we have $500(1+0.045)^2 = $500(1.045)^2 = $500(1.092)(1.092) = $500(1.189684) = $594.84.
Similarly, $500(1+0.04)^3 = $500(1.04)^3 = $500(1.1248) = $562.4.
Therefore, $500(1+0.045)^2 -$500(1+0.04)^3 = $594.84 - $562.4 = $32.44.