Exam math
Municipal bond math: tax-equivalent yield and accrued interest
Compare a tax-free coupon with a taxable one at your bracket, then work out the accrued interest a buyer pays on settlement.
Tax-equivalent yield of a muni
Taxable yield needed to match
5.15%
| Formula | muni yield / (1 - tax rate) |
| Tax-free yield | 3.50% |
| Tax rate | 32% |
The higher the bracket, the more a tax-free coupon is worth; state tax is left out here.
Two calculations come back again and again in municipal bond questions on the Series 7, 65 and 66. The first is the tax-equivalent yield: interest on most municipal bonds is free of federal income tax, so a muni yield must be grossed up before it can be compared with a taxable bond. The formula divides the muni yield by one minus the investor's marginal tax rate. A 3.5% muni is worth 5.15% taxable to someone in the 32% bracket, but only 3.98% to someone in the 12% bracket, which is why munis suit high earners and rarely fit a low-income account or an IRA, where the tax advantage is wasted. The second is accrued interest: a buyer pays the seller the interest earned since the last coupon date, up to the day before settlement. Corporate and municipal bonds count days on a 30/360 basis, every month taken as 30 days, and settle regular way one business day after the trade since the SEC moved to T+1 on May 28, 2024.
Accrued interest on a corporate or muni bond
Accrued interest per $1,000
$17.33
| Settlement (T+1) | October 15, 2026 |
| Days, 30/360 | 104 |
| Paid by | the buyer, to the seller |
Interest accrues from the last coupon date up to the day before settlement; weekends and holidays are not removed from the settlement date here.
Questions, formats and fees by Radif Partners · Editorial policy · Method
Tax-equivalent yield by bracket
| Muni yield | 12% bracket | 22% bracket | 32% bracket | 37% bracket |
|---|---|---|---|---|
| 3.00% | 3.41% | 3.85% | 4.41% | 4.76% |
| 3.50% | 3.98% | 4.49% | 5.15% | 5.56% |
| 4.00% | 4.55% | 5.13% | 5.88% | 6.35% |
The reverse question also appears: what muni yield matches a taxable bond? Multiply the taxable yield by one minus the rate. A 6% corporate bond for an investor in the 32% bracket is matched by a muni yield of 4.08%.
In-state bonds
Many states also exempt the interest of their own municipalities' bonds from state income tax. A resident who buys an in-state bond can therefore be double tax-free, while an out-of-state bond is usually taxed by the investor's home state. Questions often test this distinction without numbers.
Accrued interest, worked out
A 6% corporate bond pays coupons on January 1 and July 1. It trades on October 14, 2026 and settles one business day later, on October 15, 2026. Interest accrues from July 1 up to the day before settlement: on the 30/360 basis that is 104 days, so the buyer adds $17.33 per $1,000 bond to the price. The calculator above runs the same steps from any coupon and dates.
- Count each full month as 30 days, whatever its real length.
- Include the last coupon date, stop the day before settlement.
- Multiply the annual coupon by the days and divide by 360.
Where this sits in the outlines
The Series 7 places municipal securities and their tax treatment in the investments and recommendations function (Series 7 outline), which carries 91 of its 125 scored questions. NASAA's Series 65 and 66 guides test tax-equivalent yield within taxation and client recommendations (Series 65 guide). Settlement dates belong to the order and transaction function of the Series 7, where the move to T+1 (SEC adoption) changed the dates that older study material still shows.
Quick checks before you answer
A tax-equivalent yield is always higher than the muni yield, never lower; if your result is lower, you multiplied instead of dividing. Accrued interest is added to the price paid by the buyer and to the proceeds of the seller; it is never subtracted from either. For the plain yield measures of any bond, see the bond yield page.
General obligation and revenue bonds
Numbers aside, municipal questions turn on the source of payment. A general obligation bond is backed by the taxing power of the issuer, so its analysis looks at the tax base, debt per person and the issuer's other obligations. A revenue bond is paid from the income of a specific project, such as a toll road or a water system, so its analysis looks at the project's earnings and the protective covenants of the bond. Questions often give a description and ask which type it is, or which document an investor should read: the official statement plays for municipal issues the role a prospectus plays for corporate ones.