# Rule G-33 Calculations

## Overview

**Related Rules and Interpretations:**

(a) *Accrued Interest*. Accrued interest shall be computed in accordance with the following formula:

For purposes of this formula, the "number of days" shall be deemed to be the number of days from the previous interest payment date (from the dated date, in the case of first coupons) up to, but not including, the settlement date. The "number of days" and the "number of days in year" shall be counted in accordance with the requirements of section (e) below.

(b) *Interest-Bearing Securities*

(i)

Dollar Price. For transactions in interest-bearing securities effected on the basis of yield the resulting dollar price shall be computed in accordance with the following provisions:(A)

Securities Paying Interest Solely at Redemption. Except as otherwise provided in this section (b), the dollar price for a transaction in a security paying interest solely at redemption shall be computed in accordance with the following formula:

For purposes of this formula the symbols shall be defined as follows:

"A" is the number of accrued days from the beginning of the interest payment period to the settlement date (computed in accordance with the provisions of section (e) below);

"B" is the number of days in the year (computed in accordance with the provisions of section (e) below);

"DIR" is the number of days from the issue date to the redemption date (computed in accordance with the provisions of section (e) below);

"P" is the dollar price of the security for each $100 par value (divided by 100);

"R" is the annual interest rate (expressed as a decimal);

"RV" is the redemption value of the security per $100 par value (divided by 100); and

"Y" is the yield price of the transaction (expressed as a decimal).

(B)

Securities with Periodic Interest Payments. Except as otherwise provided in this section (b), the dollar price for a transaction in a security with periodic interest payments shall be computed as follows:(1) for securities with six months or less to redemption, the following formula shall be used:

For purposes of this formula the symbols shall be defined as follows:

"A" is the number of accrued days from the beginning of the interest payment period to the settlement date (computed in accordance with the provisions of section (e) below);

"B" is the number of days in the year (computed in accordance with the provisions of section (e) below);

"E" is the number of days in the interest payment period in which the settlement date falls (computed in accordance with the provisions of section (e) below);

"M" is the number of interest payment periods per year standard for the security involved in the transaction;

"P" is the dollar price of the security for each $100 par value (divided by 100);

"R" is the annual interest rate (expressed as a decimal);

"RV" is the redemption value of the security per $100 par value; and

"Y" is the yield price of the transaction (expressed as a decimal).

(2) for securities with more than six months to redemption, the following formula shall be used:

For purposes of this formula the symbols shall be defined as follows:

"A" is the number of accrued days from beginning of the interest payment period to the settlement date (computed in accordance with the provisions of section (e) below);

"B" is the number of days in the year (computed in accordance with the provisions of section (e) below);

"E" is the number of days in the interest payment period in which the settlement date falls (computed in accordance with the provisions of section (e) below);

"N" is the number of interest payments (expressed as a whole number) occurring between the settlement date and the redemption date, including the payment on the redemption date;

"P" is the dollar price of the security for each $100 par value;

"R" is the annual interest rate (expressed as a decimal);

"RV" is the redemption value of the security per $100 par value; and

"Y" is the yield price of the transaction (expressed as a decimal).

For purposes of this formula the symbol "exp" shall signify that the preceding value shall be raised to the power indicated by the succeeding value; for purposes of this formula the symbol "K" shall signify successively each whole number from "1" to "N" inclusive; for purposes of this formula the symbol "sigma" shall signify that the succeeding term shall be computed for each value "K" and that the results of such computations shall be summed.

(ii)

Yield. Yields on interest-bearing securities shall be computed in accordance with the following provisions:(A)

Securities Paying Interest Solely at Redemption. The yield of a transaction in a security paying interest solely at redemption shall be computed in accordance with the following formula:

For purposes of this formula the symbols shall be defined as follows:

"A" is the number of accrued days from the beginning of the interest payment period to the settlement date (computed in accordance with the provisions of section (e) below);

"DIR" is the number of days from the issue date to the redemption date (computed in accordance with the provisions of section (e) below);

"P" is the dollar price of the security for each $100 par value (divided by 100);

"R" is the annual interest rate (expressed as a decimal);

"RV" is the redemption value of the security per $100 par value (divided by 100); and

"Y" is the yield on the investment if the security is held to redemption (expressed as a decimal).

(B)

Securities with Periodic Interest Payments. The yield of a transaction in a security with periodic interest payments shall be computed as follows:(1) for securities with six months or less to redemption, the following formula shall be used:

For purposes of this formula the symbols shall be defined as follows:

"E" is the number of days in the interest payment period in which the settlement date falls (computed in accordance with the provisions of section (e) below);

"M" is the number of interest payment periods per year standard for the security involved in the transaction;

"P" is the dollar price of the security for each $100 par value (divided by 100);

"R" is the annual interest rate (expressed as decimal);

"RV" is the redemption value of the security per $100 par value; and

"Y" is the yield on the investment if the security is held to redemption (expressed as a decimal).

(2) for securities with more than six months to redemption the formula set forth in item (2) of subparagraph (b)(i)(B) shall be used.

(c) *Discounted Securities*.

(i)

Dollar Price. For transactions in discounted securities, the dollar price shall be computed in accordance with the following provisions:(A) The dollar price of a discounted security, other than a discounted security traded on a yield-equivalent basis, shall be computed in accordance with the following formula:

For purposes of this formula the symbols shall be defined as follows:

"DR" is the discount rate (expressed as a decimal);

"DSM" is the number of days from the settlement date of the transaction to the maturity date (computed in accordance with the provisions of section (e) below);

"P" is the dollar price of the security for each $100 par value; and "RV" is the redemption value of the security per $100 par value.

(B) The dollar price of a discounted security traded on a yield-equivalent basis shall be computed in accordance with the formula set forth in subparagraph (b)(i)(A).

(ii)

Return on Investment. The return on investment for a discounted security shall be computed in accordance with the following provisions:(A) The return on investment for a discounted security, other than a discounted security traded on a yield-equivalent basis, shall be computed in accordance with the following formula:

For purposes of this formula the symbols shall be defined as follows:

"DSM" is the number of days from the settlement date of the transaction to the maturity date (computed in accordance with the provisions of section (e) below);

"IR" is the annual return on investment if the security is held to maturity (expressed as a decimal);

"P" is the dollar price of the security for each $100 par value; and

"RV" is the redemption value of the security per $100 par value.

(B) The yield of a discounted security traded on a yield-equivalent basis shall be computed in accordance with the formula set forth in subparagraph (b)(ii)(A).

(d) *Standards of Accuracy; Truncation*.

(i)

Intermediate Values. All values used in computations of accrued interest, yield, and dollar price shall be computed to not less than ten decimal places.(ii)

Results of Computations. Results of computations shall be presented in accordance with the following:(A) Accrued interest shall be truncated to three decimal places, and rounded to two decimal places immediately prior to presentation of total accrued interest amount on the confirmation;

(B) Dollar prices shall be truncated to three decimal places immediately prior to presentation of dollar price on the confirmation and computation of extended principal; and

(C) Yields shall be truncated to four decimal places, and rounded to three decimal places,

provided, however, that for purposes of confirmation display as required under rule G-15(a) yields accurate to the nearest .05 percentage points shall be deemed satisfactory.Numbers shall be rounded, where required, in the following manner: if the last digit after truncation is five or above, the preceding digit shall be increased to the next highest number, and the last digit shall be discarded.

(e) *Day Counting.*

(i)

Day Count Basis. Computations under the requirements of this rule shall be made on the basis of a thirty-day month and a three-hundred-sixty-day year, or, in the case of computations on securities paying interest solely at redemption, on the day count basis selected by the issuer of the securities.(ii)

Day Count Formula. For purposes of this rule, computations of day counts on the basis of a thirty-day month and a three-hundred-sixty-day year shall be made in accordance with the following formula.

**Number of Days = (Y2 - Y1) 360 + (M2 - M1) 30 + (D2 - D1)**

For purposes of this formula the symbols shall be defined as follows:

"M1" is the month of the date on which the computation period begins;

"D1" is the day of the date on which the computation period begins;

"Y1" is the year of the date on which the computation period begins;

"M2" is the month of the date on which the computation period ends;

"D2" is the day of the date on which the computation period ends; and

"Y2" is the year of the date on which the computation period ends.

For purposes of this formula, if the symbol "D2" has a value of "31," and the symbol "D1" has a value of "30" or "31," the value of the symbol "D2" shall be changed to "30." If the symbol "D1" has a value of "31," the value of the symbol "D1" shall be changed to "30." For purposes of this rule time periods shall be computed to include the day specified in the rule for the beginning of the period but not to include the day specified for the end of the period.