delivered the opinion of the court:
Plaintiffs, Lowell and Carol Kousins, appeal from the order of the circuit court of Lake County dismissing their amended complaint seeking relief from the alleged illegal assessment of a real estate tax penalty.
The issue presented on appeal is whether the trial court lacked jurisdiction to consider the claim raised in plaintiffs’ complaint.
Plaintiffs were assessed real estate taxes for 1984 in the amount *773of $3,856.98 to be paid in two equal installments of $1,928.49. The first installment was due on June 2, 1985, and the second installment was due on September 3, 1985. Plaintiffs paid the first installment on July 12,1985.
On or about July 21, 1985, plaintiffs received notice that they were being charged a penalty of $57.85 because their payment was late. The penalty was calculated at a lV2%-per-month rate on the $1,928.49 first installment for the entire months of June and July. Plaintiffs paid the $57.85 penalty on July 21, 1985.
Plaintiffs filed an amended class action complaint contending, inter alia, that any penalty imposed after the July 12, 1985, date of payment of the first installment is unauthorized by law and seeking injunctive and declaratory relief. The circuit court, on June 22, 1988, granted defendants’ motion to dismiss with prejudice, finding that it lacked jurisdiction to consider plaintiffs’ claim because plaintiffs had an adequate remedy at law and because plaintiffs’ claim did not establish that the complained-of penalty was unauthorized by law.
On June 29, 1988, defendants filed a motion for attorney fees and costs pursuant to section 2 — 611 of the Civil Practice Law (Ill. Rev. Stat. 1987, ch. 110, par. 2 — 611). On July 11, 1988, plaintiffs moved to dismiss defendants’ section 2 — 611 motion and filed a cross-motion for attorney fees and costs pursuant to section 2 — 611. Plaintiffs appealed only from the order dismissing their amended complaint, and this court dismissed the appeal because there was no finding pursuant to Supreme Court Rule 304(a) (107 Ill. 2d R. 304(a)) making the dismissal order final and appealable. (Kousins v. Anderson (1989), 180 Ill. App. 3d 827, 536 N.E.2d 487.) On remand, the circuit court entered an agreed order dismissing the parties’ section 2 — 611 cross-petitions, and this appeal ensued.
The usual vehicle for challenging tax assessments is the legal remedy provided by statute for paying taxes under protest and filing objections to the application for judgment. (Clarendon Associates v. Korzen (1973), 56 Ill. 2d 101, 104, 306 N.E.2d 299.) Independent grounds for equitable jurisdiction in real estate tax cases exist only when no adequate legal remedy is available, when exempt property is taxed, or when an unauthorized tax is levied. (First National Bank & Trust Co. v. Rosewell (1982), 93 Ill. 2d 388, 392, 444 N.E.2d 126; see also Schlenz v. Castle (1986), 115 Ill. 2d 135, 141, 503 N.E.2d 241.) The two latter situations constitute independent grounds for equitable relief, and, in such cases, it is not necessary that the remedy at law be inadequate. (Clarendon Association, 56 Ill. 2d at 105, 306 N.E.2d at 301.) As to the unauthorized-by-law exception, the question is not *774whether the tax is valid but, rather, whether the assessor has the power to function. (North Pier Terminal Co. v. Tully (1976), 62 Ill. 2d 540, 548, 343 N.E.2d 507.) The challenge must be to the assessor’s authority to act in order to sustain equitable jurisdiction. North Pier Terminal Co., 62 Ill. 2d at 548, 343 N.E.2d at 511.
In this case, plaintiffs contend that the county collector improperly imposed a penalty on their late first installment by assessing a V-k% penalty for the entire month of July rather than applying that rate on a pro rata basis through July 12 only. In other words, plaintiffs argue that because the first installment was paid on July 12, it was no longer unpaid and late and therefore the county collector lacked statutory authority to assess a penalty based on a late payment beyond that date.
Section 224 of the Revenue Act of 1939 states in pertinent part:
Ҥ224. All dates on which unpaid taxes become delinquent under this Section shall be subject to modification by ordinance of the county board as provided in Section 224.1b of this Act.
All real estate upon which the first installment of taxes for years subsequent to the year 1950 remains unpaid on the first day of June annually shall be deemed delinquent as to such first installment and except as may be provided pursuant to section 224.1, and such unpaid first installment shall bear interest after the first day of June annually (a) after the effective date of this amendatory Act of 1985 and before January 1, 1989, at the rate of 1% per month for all real property, and (b) before the effective date of this amendatory Act of 1985 and again on and after January 1, 1989, at the rate of 1%% per month for all real property until paid or forfeited ***.” Ill. Rev. Stat. 1985, ch. 120, par. 705.
Accordingly, section 224 provides the authority for the county collector to assess an interest penalty on an “unpaid first installment *** until paid or forfeited.” Plaintiffs’ complaint alleges that the county collector does not have the authority to collect the applicable 1V2% interest penalty for any period beyond the date the real estate tax payment is made. Thus, plaintiffs’ complaint challenges the authority of the county collector to assess the interest penalty for the entire month of July when plaintiffs paid the first installment on July 12. Such allegations go to the power of the collector to assess the interest penalty, rather than merely challenging whether the interest penalty was calculated properly. Thus, plaintiffs’ claim falls within the unauthorized-by-law exception, and the circuit court has jurisdiction to consider plaintiffs’ claim.
*775Although our research reveals no case deciding this precise issue, we are persuaded by a decision of the appellate court under similar circumstances. In W.F. Smith & Co. v. Rosewell (1984), 123 Ill. App. 3d 939, 463 N.E.2d 1024, the court held that the assessment of costs is purely statutory and depends entirely upon the terms of the statute authorizing them. (123 Ill. App. 3d at 944, 463 N.E.2d at 1028.) In a case where a plaintiff challenges the assessment of costs as exceeding the amount authorized by statute, the excess costs assessed are within the definition of a tax unauthorized by law. (123 Ill. App. 3d at 944, 463 N.E.2d at 1028.) Thus, the county collector lacks power and authority to impose charges for costs in excess of the amount of costs authorized by statute, and the circuit court has jurisdiction to hear such a claim. (123 Ill. App. 3d at 944, 463 N.E.2d at 1028.) Similarly, in the present case, any interest penalty assessed beyond that authorized by statute would be beyond the power and authority of the county collector, and plaintiffs’ claim to that effect invoked the equitable jurisdiction of the court.
The judgment of the circuit court of Lake County is reversed, and this cause is remanded for further proceedings on the amended complaint.
Reversed and remanded.
UNVERZAGT, P.J., and WOODWARD, J., concur.