
90 S.W.3d 169 (2002)
Edward J. PUISIS, Petitioner/Appellant,
v.
Kim A. PUISIS, Respondent/Respondent.
No. ED 80934.
Missouri Court of Appeals, Eastern District, Division Four.
October 22, 2002.
*170 Benjamin Frederick Lewis, Vogel, Layton & Lewis Law Firm, Cape Girardeau, MO, for Appellant.
Allen E. Moss Jr., Finch & Moss Law Firm, Cape Girardeau, MO, for Respondent.
SHERRI B. SULLIVAN, Judge.

Introduction
Edward J. Puisis (Father) appeals from a trial court judgment modifying a decree of divorce entered by the Court of Common Pleas of Erie County, Pennsylvania. We affirm.

Factual and Procedural Background
The Court of Common Pleas of Erie County, Pennsylvania entered a decree of divorce dissolving the marriage of Father and Kim A. Puisis (Mother) on September 1, 1994. Two children were born of the marriage. J.P. was born in April 1987 and A.P. was born in August 1989. The decree of divorce did not make child custody, *171 visitation, or support orders,[1] although the children have remained in Mother's physical custody since the divorce, subject to visitation with Father on such terms as the parties have, from time to time, been able to agree. In June 2000, Mother moved with the children to Missouri. Missouri is now the home state for the children.
In July 2001, Father filed a Motion to Modify Judgment and Decree of Dissolution of Marriage (Motion to Modify) requesting the trial court to order joint legal and physical custody of the children, with J.P.'s primary residence to be with Father and A.P.'s primary residence to be with Mother, subject to the terms of a parenting plan attached to the motion.
On November 19, 2001, after a hearing, the trial court entered a judgment (Original Judgment) on Father's Motion to Modify. The Original Judgment awarded joint legal custody of the children to Father and Mother and primary physical custody of the children to Mother, subject to a minimum schedule of visitation.
On December 3, 2001, Mother filed a Motion to Vacate, Set Aside or Amend Judgment (Motion to Amend) arguing that the Original Judgment did not represent the trial court's ruling on the matter and did not set out all the terms and conditions that the trial court directed. On February 7, 2002, Father filed a Motion for New Trial.
On February 14, 2002, after a hearing, the trial court entered a First Revised and Amended Judgment and Order for Modification of Visitation (Amended Judgment). The Amended Judgment denied a modification of the physical custody of the children but granted a modification of visitation rights. The Amended Judgment refers to the hearing held on Father's Motion to Modify but not on Mother's Motion to Amend, except in stating that "any and all other motions for relief filed by either party shall be denied."
On March 14, 2002, Father filed another Motion for New Trial. On March 20, 2002, Father filed his notice of appeal.

Discussion
Father raises two points on appeal. We address his second point first as it raises a jurisdictional question. In his second point, Father argues that the trial court was without jurisdiction to enter the Amended Judgment on February 14, 2002 because Mother failed to file a motion for new trial and thus the court's jurisdiction over the Original Judgment expired thirty days after it was entered on November 19, 2001.
In cases tried without a jury, a party may file a motion for new trial or a motion to amend the judgment not later than thirty days after the entry of judgment. Rule 73.01(d); Rule 78.04.[2] The trial court retains control over judgments during the thirty-day period after entry of judgment and may, after giving the parties an opportunity to be heard and for good cause, vacate, reopen, correct, amend or modify its judgment within that time. Rule 75.01. Any motion for new trial or motion to amend the judgment is overruled for all purposes if the trial court does not rule on it within ninety days after the last such timely motion is filed. Rule 78.06.
Rule 81.05(a)(2) provides:
If a party timely files an authorized after-trial motion, the judgment becomes *172 final at the earlier of the following:
(A) Ninety days from the date the last timely motion was filed, on which date all motions not ruled shall be deemed overruled; or
(B) If all motions have been ruled, then the date of ruling of the last motion to be ruled or thirty days after entry of judgment, whichever is later.
Rules 78.06 and 81.05 allow for the extension of the trial court's control over a judgment from thirty days to ninety days after a timely authorized after-trial motion is filed. Klaus v. Shelby, 4 S.W.3d 635, 637 (Mo.App. E.D.1999). During the ninety-day period, the trial court has the same control over the judgment as under Rule 75.01. Id.
Under the Missouri Supreme Court Rules, an authorized after-trial motion is a motion for which the rules expressly provide. Taylor v. United Parcel Serv., Inc., 854 S.W.2d 390, 393 n. 1 (Mo. banc 1993). Currently, the rules expressly provide for a motion to amend the judgment. Rule 73.01(d); Rule 78.04.
The trial court entered the Original Judgment on November 19, 2001. Mother timely filed her Motion to Amend, an authorized after-trial motion,[3] within thirty days after the entry of the Original Judgment. Accordingly, the trial court's control over the Original Judgment extended to ninety days, during which time the trial court retained the same power as under Rule 75.01. The trial court entered the Amended Judgment on February 14, 2002, within ninety days from the filing of Mother's Motion to Amend. Therefore, the trial court had jurisdiction to enter the Amended Judgment. Accordingly, Father's point two on appeal is denied.[4]
Returning to Father's first point on appeal, Father argues that the trial court erred in finding as a matter of law that Father failed to prove a change of circumstances sufficient for the court to consider a modification of custody.
At the close of Father's case, the trial court, on its own motion, entered judgment in favor of Mother. In the Amended Judgment, the trial court found the following:
The Court finds, as a matter of law, that [Father] has failed to prove facts which have arisen since the prior decree or which were unknown to the Court at the time of the prior decree, that a change has occurred in the circumstances of the minor children or their custodian and that modification of physical custody is necessary to serve the best interests of the children.
Section 452.410[5] provides in pertinent part:
[T]he court shall not modify a prior custody decree unless ... it finds, upon the basis of facts that have arisen since the prior decree or that were unknown to the court at the time of the prior decree, that a change has occurred in the circumstances of the child or his custodian *173 and that the modification is necessary to serve the best interests of the child.
Section 452.411 provides:
If either parent of a child changes his residence to another state, such change of residence of the parent shall be deemed a change of circumstances under section 452.410, allowing the court to modify a prior visitation or custody decree.
Since the decree of divorce, Mother remarried and moved with the children from Pennsylvania to Missouri. Father also remarried and, for voluntary job changes, moved from Pennsylvania to Tennessee to Kentucky.[6] Thus, under the plain language of Section 452.411, a change of circumstances under Section 452.410 has occurred. However, even if the trial court erred in finding that Father failed to prove a change in circumstances sufficient to allow a modification of custody, we may still affirm the Amended Judgment.[7]
Although a change of circumstances under Section 452.411 allows the trial court to modify custody, it does not require a modification. In addition to finding a change of circumstances, Section 452.410 requires a finding that a modification is necessary to serve the best interests of the child. There is no fixed test for determining the best interests of the child when modifying a child custody decree under the general standard set forth in Section 452.410. Bohac v. Akbani, 29 S.W.3d 407, 412 (Mo.App. E.D.2000).
The trial court determines what is in the best interests of the child and we determine whether there is evidence to support that assessment. Lavalle v. Lavalle, 11 S.W.3d 640, 646 (Mo.App. E.D.1999). We will not reverse a trial court's custody decision unless the party moving for a modification demonstrates that the decision was not in the best interests of the child. Larkins v. Larkins, 921 S.W.2d 152, 153 (Mo.App. E.D.1996).
In the Amended Judgment, the trial court found the following:
[I]t would not be in the children's best interest to change physical custody of the minor children from [Mother] to [Father]....[T]he children are doing very well in their current environment. The children are well adjusted to their home, family and school.
We find that Father has not met his burden of showing that the trial court's custody decision is not in the children's best interests. Father testified that both children have done well academically. J.P. receives grades of "A's and maybe an occasional B." J.P. is in good health and plays basketball. Father's job rarely allows him to leave work during the day, and so he would be unavailable to transport the children to activities or to attend school functions regularly. Mother's job allows her the freedom "to take the kids from here to there." Mother has been the primary caretaker for the children since the divorce.
The record on appeal supports the trial court's assessment of the children's best *174 interests. Accordingly, Father's point one on appeal is denied.

Conclusion
The Amended Judgment of the trial court is affirmed.
WILLIAM H. CRANDALL, JR., P.J., and GLENN A. NORTON, J., concur.
NOTES
[1]  An administrative order for support was entered during the pendency of the divorce and modified in 1995.
[2]  All rule references are to Mo. R. Civ. P.2002, unless otherwise indicated.
[3]  We note that Mother's Motion to Amend did not specifically and expressly invoke Rule 75.01. We therefore construe the motion as being filed under Rule 73.01(d).
[4]  In his reply brief, Father alleges that the trial court also erred in entering the Amended Judgment because Mother's Motion to Amend was insufficient. Father did not raise this allegation of error in his initial brief. Allegations of error not raised in the initial brief are not preserved for appellate review because a respondent has no opportunity to address the argument. Coyne v. Coyne, 17 S.W.3d 904, 906 (Mo.App. E.D.2000).
[5]  All statutory references are to RSMo. (2000), unless otherwise indicated.
[6]  Prior to moving to Tennessee, Father had a temporary residence in Indiana while he maintained his residence in Pennsylvania.
[7]  We note that our concern is with the correctness of the result reached, not the route taken to reach that result. Vilsick v. Standard Insulations, Inc., 926 S.W.2d 499, 501 (Mo.App. E.D.1996). A court-tried case that reaches a correct result will not be reversed even if the trial court gives a wrong or insufficient reason for its judgment. Holdener v. Fieser, 971 S.W.2d 946, 950 (Mo.App. E.D.1998). We review a case on the whole record and will affirm the judgment if any proper grounds exist within the record. Id.
