
409 S.W.2d 546 (1966)
COMMUNITY SAVINGS AND LOAN ASSOCIATION, Petitioner,
v.
R. L. FISHER et ux., Respondents.
No. A-11429.
Supreme Court of Texas.
October 19, 1966.
Rehearing Denied December 31, 1966.
*547 Raymond Kneese, Fredericksburg, Bryce A. Taylor, Burnet, Moursund & Ferguson, Johnson City, for petitioner.
Harold Kennedy, Austin, for respondents.
WALKER, Justice.
This is an action for a declaratory judgment to determine the balance unpaid on a promissory note. There is no dispute as to the dates and amounts of the payments that have been made, and the case turns upon the rate of interest and the manner in which the same accrues and is payable under the terms of the loan instruments.
On June 23, 1960, R. L. Fisher and wife, respondents, borrowed $7,200.00 from Fredericksburg Savings and Loan Association, now Community Savings and Loan Association, petitioner. As evidence of the indebtedness, they executed to petitioner their note in the face amount of $10,800.00 and secured the same by a deed of trust on real estate in Burnet County. The material provisions of the note are as follows:
"$10,800.00 Fredericksburg, Texas, June 23, 1960
"* * * pay to the order of Fredericksburg Savings and Loan Association * * * the sum of TEN THOUSAND EIGHT HUNDRED AND NO/100 ($10,800.00) DOLLARS, which includes *548 interest for the stated period, in 120 monthly installments as follows:
"$90.00 on the 1st day of August, 1960, and the same amount on the same day of each succeeding month thereafter, except that the final payment shall be the unpaid balance then due on the note * * *. In event of prepayment of the entire balance before maturity, the holder agrees to credit to said note all unearned interest, however, there will be a prepayment expense charge not to exceed $75.00.
"* * * Interest included in the face amount of this note not earned at the date of acceleration shall be cancelled and credited upon this note. The holder hereof shall never be entitled to receive or collect interest at a rate in excess of ten per cent per annum on the principal indebtedness * * *
* * * * * *
"The original net amount of this note is $7,200.00."
The deed of trust provides that the monthly payments on the note shall be applied: first, to the liquidation of any incidental expenses representing a part of the loan; next, to insurance premiums, taxes and assessments against the property; and "then regularly to the interest on the unpaid balance and the remainder to principal until said note is paid in full." No rate of interest was specified in either the note or the deed of trust. As part of the transaction in which these instruments were executed and the proceeds of the loan disbursed, petitioner furnished respondents a loan closing statement which reads, in part, as follows:
        "We submit herewith for your information the terms of the loan,
    and the expenses thereof, whether charged to you by the association,
    or paid for you by the association.
        "Loan No. ______              Amount $7,200.00    Rate of Interest
                                                             Disc - 5%
        "Each monthly payment of $90.00 plus 1/12 annual taxes and 1/12
    annual hazard insurance is due the 1st day of each month, beginning on
    August 1, 1960."
The loan was made for petitioner by one of its officers, Reuben Eckhardt. He stated that the $3,600.00 interest added to the face of the note was computed by charging 5% of the original $7,200.00 principal for each of the ten years the loan would have been outstanding if it ran to maturity. According to his testimony, the term "Disc-5%" appearing on the loan closing statement means that interest calculated in this manner has been added to the face amount of the note. Respondent R. L. Fisher was told that he would be made a five per cent discount loan, but he did not know the difference between that type of loan and one in which the stated percentage represents the effective interest rate.
Respondents notified petitioner that they wished to pay the balance of the note on October 1, 1964. At that time the loan had run 51 months, and respondents had paid a total of $8,584.93 on the note. They concluded that the earned interest would be 5% per annum on $7,200.00 for 51 months, or a total of $1,530.00. On this basis the unearned interest amounted to $2,070.00, and the balance unpaid on the note was $145.07. This amount plus the $75.00 prepayment charge was tendered to petitioner as constituting full payment of the note.
By the use of its tables prepared for that purpose, petitioner determined that the unpaid principal balance of the loan was $874.09. On the basis of this figure, with adjustments *549 for the September interest, the prepayment fee, and the balance held in escrow to pay taxes and insurance, the amount required to retire the loan was $800.29. When petitioner insisted upon payment of that amount, respondents instituted the present suit. The trial court adopted respondents' theory as to the proper method of determining the unearned interest and entered judgment accordingly, and the Court of Civil Appeals at Austin affirmed. 400 S.W.2d 927.
The intermediate court held that the unearned interest should be computed on the same basis as the amount of interest included in the face of the note was calculated at the inception of the loan. We have jurisdiction under Subdivisions 2 and 3 of Article 1728.[1] The construction of Article 5070 is necessary to a determination of the case, and the above mentioned holding of the Court of Civil Appeals is in conflict with the decision of the Court of Civil Appeals at Amarillo in American Nat. Ins. Co. v. Schenck, Tex.Civ.App., 85 S.W.2d 833 (no writ).
Respondents argue that the rights of the parties are governed by the "rate of interest" set out in the loan settlement statement. They suggest that if this is not so, then no rate of interest has been specified and petitioner is entitled to charge six per cent per annum under the provisions of Article 5070. We do not agree. Respondents may well have been misled by the loan settlement statement, but there is no claim of fraud and no effort to obtain equitable relief. While the statement purports to set out the terms of he loan, it is not contractual in a nature and not a part of the integrated loans contract represented by the note and deed of trust. Its recitals may be considered with the other surrounding circumstances in construing the agreement, but the rights and obligations of the parties must be determined from their contract. In this instance there is no ambiguity or doubt as to the legal effect of the note and deed of trust, and the same may not be added to or varied by expressions found in the contemporaneous but extrinsic writing. See McCormick and Ray, Texas Law of Evidence, 2nd ed. 1956, § 1601.
The note in Schenck contained no provision for rebating interest upon acceleration of maturity and no stipulation that the holder would never be entitled to interest in excess of ten per cent per annum, but was similar in all other material respects to the note involved in the present case. The plaintiff there contended on appeal that, independent of the acceleration of maturity provisions, the interest contracted for over the full term of the loan was more than ten per cent per annum. The Court of Civil Appeals first pointed out that this position had not been taken in the court below, and that on appeal the parties are restricted to the theory on which the case was tried. It then proceeded to discuss the contention, evidently for the guidance of the trial court upon remand and in connection with its holding that the exclusion of certain testimony was erroneous. The following portion of the opinion is relevant here:
"* * * In cases of this character, where interest is included in the face of the note and it is to be discharged by partial payments made at stated intervals, the rule for computing the interest and applying the payments is announced by the Supreme Court to be as follows: `When partial payments are made, interest is to be computed to the time when a payment alone, or in conjunction with preceding payments, shall equal or exceed the interest due. Then deduct the payment and calculate the interest on the balance until the next payment or payments as before, and so on.' Odle v. Frost, 59 Tex. 684; Hampton v. Dean, 4 Tex. 455; Hearn v. Cutberth, 10 Tex. 216; Clark v. Brown, 48 Tex. 212.
*550 "The rate of interest which the makers should pay in discharging the note is not stated either in the face of the note or in the mortgage securing same, but the amount of principal, together with the amount of interest and amount of payments necessary to discharge the indebtedness, being shown, a calculation discloses that interest was charged at the rate of eight and a fraction per cent. per annum. The testimony bearing upon this issue was excluded, and we think this action of the court is error."
When the parties do not agree otherwise, partial payments on an interest-bearing obligation are ordinarily applied first to accrued interest and the balance to principal. Each succeeding payment is credited in a similar manner with the interest computed on the balance of the principal remaining unpaid. This is the so-called United States rule, which is recognized in Texas. See Tooke v. Bonds, 29 Tex. 419; J. I. Case Co. v. Laubhan, Tex. Civ.App., 64 S.W.2d 1079 (no writ); 30 Am.Jur. Interest § 49; 47 C.J.S. Interest § 66; and authorities cited above. The rule is applicable to an add-on note payable in monthly installments such as we have in the present case, and in this instance the parties so stipulated in the deed of trust.
Here the interest charge is part of the face amount of the note, and the rate of interest is not stated in the loan contract. Under these circumstances the true interest rate must be determined by calculation. It is that percentage which, when applied to each monthly balance of the principal will, upon crediting the payments in accordance with the rule stated above, result in complete amortization of the $7,200.00 principal advance and the $3,600.00 interest charge in 120 monthly payments of $90.00 each as agreed by the parties. See Ustick v. Jones, 130 Tex. 620, 112 S.W.2d 703; Braniff Inv. Co. v. Robertson, 124 Tex. 524, 81 S.W.2d 45, 100 A.L.R. 1421; Bohannan v. First Nat. Bank in Dallas, Tex.Civ.App., 85 S.W.2d 989 (wr. ref.); Federal Mortgage Co. v. Davis, Tex.Civ.App., 100 S.W.2d 717 (affirmed, Davis v. Federal Mortgage Co., 131 Tex. 46, 111 S.W.2d 1066). Where all of the essential terms have thus been stated and determination of the rate of interest is merely a matter of calculation under applicable rules of law, this constitutes an agreement for a "specified rate of interest" and Article 5070 has no application.[2] The note in the present case stipulates that the final installment shall be the balance unpaid, but that provision is to be disregarded in computing the interest rate.
The witness Eckhardt testified that petitioner determined the unearned interest by the sum of the digits method and with the use of standard tables. He also explained that:
"This is a method whereby it closely resembles simple interest. In other words, when your loan balance is raised, higher percentage of interest is returned; as your principal decreases, interest decreases, and it is figured according to the number of years the loan has to run. Each number of years has a separate chart we go by."
Neither the trial court nor the Court of Civil Appeals was given any further explanation of the sum of the digits method, and the tables referred to by the witness were not introduced in evidence. The sum of the digits or direct ratio method is based upon a false assumption and yet produces a result that is quite close to the true interest rate determined in accordance with the rules set out above. According to one authority, the two figures "would be interchangeable *551 for all practical purposes except in financial transactions in which very large amounts are involved." Neifeld's Guide to Instalment Computations, p. 183, 190.
Petitioner has now calculated the true interest rate on the note in this case at 8.69 per cent per annum. Our computations based upon interest tables yielded substantially the same result. See Lake's Monthly Installment and Interest Tables, 5th ed. 1949, p. 219. The rate determined by the sum of the digits formula is 8.52 per cent per annum, which is somewhat more advantageous to respondents than the true rate. See Neifeld, Supra, p. 185. Attached to the application for writ of error is a schedule prepared by petitioner showing that when interest is charged at the rate of 8.69 per cent per annum, 120 monthly payments of $90.00 each will amortize a loan in the original principal amount of $7,200.00. When unearned interest is credited in accordance with this schedule, the amount necessary to liquidate respondents' loan as of October 1, 1964, was lightly more than the amount demanded by petitioner. It thus appears as a matter of law that the trial court erred in failing to render judgment on the basis of petitioner's figures, but those figures are now subject to adjustment for interest accruing after October 1, 1964, and any other debits or credits properly made to the account subsequent to that date.
Although respondents argue to the contrary, they are not entitled to have earned interest computed on the balance of the principal remaining unpaid from time to time after their advance payments are credited thereon. The monthly installments on the note are not payable "on or before" the stipulated maturity dates, and the only prepayment privilege is with respect to the entire balance of the note.
The judgments of the courts below are reversed, and the cause is remanded to the district court.

ON MOTION FOR REHEARING
In their motion for rehearing, respondents point out that while they had no legal right to pay the monthly installments on the note in advance, the association has accepted partial payments made prior to maturity. They insist that each payment so made should be credited in accordance with the so-called United States rule, and that interest would thereafter accrue only on the principal balance remaining unpaid. No decisions bearing directly on this question are cited by either party, and we have found relatively few.
The bond in Spires v. Hamot, 8 Watts & S. 17 (Pa.1844), was payable "on or before" ten years after date with lawful interest, but the fact that the debtor had the right to make payments in advance of maturity apparently was not regarded as significant. In holding that advance payments should be applied first to accrued interest and the remainder to principal, the court said:
"A creditor may refuse to receive the principal before it is due, or a part of it when due, except on his own terms; and were he to receive it as a payment bearing interest, it would, in effect, be a loan. But if he receive it unconditionally, the residue applied to the principal, after payment of the interest, stops interest on the principal pro tanto."
In Jencks v. Alexander, 11 Paige's Ch. 619 (N.Y.1845), the principal of the note was payable in five equal annual installments, and the interest was also payable annually. The following rules were announced for crediting payments made in advance of maturity:
"* * * where principal is not due, but interest is due, the payment must be applied to the extinguishment of the interest then due and payable, and the residue to the extinguishment of that part of the principal which will first become due; so as to stop the interest, pro tanto, from the time of such payment. But *552 where neither principal nor interest has become due at the time of the payment, such payment, in the absence of any agreement as to the application, is to be applied to the extinguishment of principal and interest, rateably; according to the decision of the supreme court in the case of Williams v. Houghtaling [& Bevier], (3 Cowen's Rep. 86)."
The situation of the parties is somewhat different where interest has been paid in advance or included in the face amount of the note. In Skelly v. Bristol Savings Bank, 63 Conn. 83, 26 A. 474, 19 L.R.A. 599, the note was payable on demand and stipulated that interest would be paid semi-annually in advance. It was held that full payment of the principal prior to the date to which interest had been paid did not entitle the debtor to recover the unearned interest. The court pointed out that there was no express promise to return unearned interest, and concluded that such a promise could not fairly be inferred under the circumstances.
In Pool v. First Nat. Bank of Princeton, 287 Ky. 684, 155 S.W.2d 4, the first year's interest was included in the face of the note. The note was payable one year after date with interest from maturity, and payments were made thereon before the note was due. The maker claimed that he was entitled to a rebate of interest on the amount of each payment from the date of such payment to the due date of the note. This claim was denied, and the court said:
"It will be assumed that the loan would not have been made had it not been for an agreement on the part of the debtor to pay the exact amount of interest recited in the contract, and, the parties having entered into a specific contract to that effect, the court will not make a new contract for them. Especially is it true where the debtor includes the amount of the interest in the face of the note, thus merging the interest with the principal and designating it for all purposes to be a part of the principal."
Interest was included in the face amount of the note in the present case. According to the terms of the instrument additional interest was to accrue only after maturity. Respondents unconditionally promised to pay 120 monthly installments of $90.00 each, and the only stipulation for rebate of interest is in the event of prepayment of the entire balance of the note. The parties thus expressly dealt with the effect of advance payments upon the interest included in the note, and made no provision for any rebate in the event of partial payments prior to maturity. It is our opinion that in these circumstances such partial payments do not entitle respondents to a rebate of interest.
The motion for rehearing is overruled. Respondents will have fifteen days from this date within which they may file another motion for rehearing if they so desire.
NOTES
[1]  All statutes are referred to by the article number under which they appear in Vernon's Annotated Texas Civil Statutes.
[2]  Article 5070. When no specified rate of interest is agreed upon by the parties, interest at the rate of six per cent per annum shall be allowed on all written contracts ascertaining the sum payable, from and after the time when the sum is due and payable; and on all open accounts, from the first day of January after the same are made.
