SIE exam math: formulas with examples

The SIE is mostly a vocabulary and rules exam, but a handful of questions are pure arithmetic, and those are the easiest points to lock in. Every example below comes from Encodr's SIE course, with the arithmetic shown. Figures marked "as of 2026" can change.

1. Bond price and yield

Price and yield move in opposite directions. When market rates rise, an existing bond's price falls and the yield to a new buyer rises. A bond priced below par (a discount) has a yield to maturity above its coupon rate; at par they are equal; above par (a premium) the yield is below the coupon.

Example: a 10-year, 4 percent, $1,000 bond is priced at par. Market yield rises from 4 to 5 percent, and the new price is $922.05, a drop of 7.79 percent. Two more facts follow from the same example set:

• A 2 percent coupon bond with the same maturity falls 8.58 percent for the same 1 point rise, more than the 4 percent bond's 7.79 percent. Lower coupons are more sensitive.
• The same 1 point rise drops a 4 percent bond's price 4.38, 7.79 and 15.45 percent at 5, 10 and 30 years. Longer maturities carry more interest rate risk.

Know the direction of yield to maturity too: the 4 percent, 10-year bond priced at $899.37 has a yield to maturity of 5.31 percent, above its coupon, as a discount bond should.

2. Current yield

Current yield = annual interest / current market price. Use the price, not par.

• An 8 percent, $1,000 par bond priced at 90 ($900): $80 / $900 = 8.89 percent.
• A 5 percent coupon bond ($50 a year) priced at $950: 50 / 950 = 5.26 percent.
• The same bond at $1,050: 50 / 1,050 = 4.76 percent. A premium price pushes current yield below the coupon.

For a discount bond the ordering is coupon < current yield < yield to maturity. Example: a 5 percent coupon, current yield 5.56 percent ($50 / $900), yield to maturity 6.37 percent.

Check your own numbers in the bond yield calculator.

3. Tax-equivalent yield

Tax-equivalent yield = tax-exempt yield / (1 - tax bracket). It tells you what a taxable bond would have to pay to match a municipal bond after tax.

• 3.00 percent muni, 37 percent bracket: 3.00 / (1 - 0.37) = 3.00 / 0.63 = 4.76 percent.
• 4.50 percent muni, 24 percent bracket: 4.50 / (1 - 0.24) = 4.50 / 0.76 = 5.92 percent.

The break-even bracket for a 4.00 percent muni against a 6.00 percent taxable bond is 1 - 4/6 = 33.3 percent, and above that bracket the muni is better after tax. Check at 35 percent: 6.00 x (1 - 0.35) = 3.90 percent, which is less than 4.00.

4. Option breakeven, profit and loss

One standard contract covers 100 shares, and a premium is quoted per share.

• Long call: breakeven = strike + premium. Strike 50, premium 3.00: 50 + 3 = 53. Maximum loss is the premium, 3.00 x 100 = $300.
• Long put: breakeven = strike - premium. Strike 50, premium 4.00: 50 - 4 = 46.
• Long 50 call bought for 3.00, stock at 58 at expiration: (58 - 50 - 3.00) x 100 = $500 profit.
• Short put, strike 40, premium received 1.80: maximum loss is (40 - 1.80) x 100 = $3,820.
• Covered call: stock bought at 48.00, one 50 call sold for 2.00. Breakeven is 48 - 2 = 46. Maximum gain is (50 - 48 + 2) x 100 = $400.
• Protective put: stock at 60.00, a 58 put bought for 1.50. Breakeven is 60 + 1.50 = 61.50, and maximum loss is (60 - 58 + 1.50) x 100 = $350.

The options profit calculator draws these payoffs, and SIE options basics with worked examples explains each position.

5. NAV and public offering price

NAV per share = (total assets - total liabilities) / shares outstanding. A fund with $250,000,000 in assets, $10,000,000 in liabilities and 12,000,000 shares has a NAV of $240,000,000 / 12,000,000 = $20.00.

The public offering price (POP) is NAV plus the sales charge, and the charge is a percentage of the POP, not of NAV. So POP = NAV / (1 - sales charge).

• NAV $20.00, 5 percent charge: 20.00 / 0.95 = $21.05.
• Going backward: NAV $11.40 and POP $12.00 give a charge of (12.00 - 11.40) / 12.00 = 5 percent.

Putting $10,000 into the $10.00 POP fund buys 10,000 / 10.00 = 1,000 shares, and $9,500 (1,000 x $9.50) works in the fund. The mutual fund sales charge calculator does this for you.

6. Dividend yield and splits

Dividend yield = annual dividend / share price. A $2.00 annual dividend on a $50 stock is 2 / 50 = 4 percent.

and stock dividends

A split changes the share count and the price, but the total value stays the same.

• 2-for-1 on 100 shares at $60: 200 shares at $30. Value stays $6,000.
• 1-for-5 reverse split on 500 shares at $2.00: 500 x 1/5 = 100 shares at $10.00. Value stays $1,000.

7. Margin equity

As of 2026, Regulation T sets the initial requirement at 50 percent, and FINRA Rule 4210 sets the 25 percent maintenance requirement. Equity = market value - debit balance.

• Buying $20,000 of stock: 50 percent x $20,000 = $10,000 deposit.
• Debit balance $10,000, market value $14,000: equity is $4,000. The 25 percent requirement is $3,500, so no call.
• Market value falls to $12,000: equity is $2,000, the requirement is 25 percent x $12,000 = $3,000, and the call is $1,000.
• The call point is where equity equals 25 percent: value = $10,000 / 0.75 = $13,333.33.

The margin account calculator shows each step.

Practice, don't just read

Write the formula first, then the numbers. Encodr's free FINRA SIE course has calculation cards for every topic here, with typed answers so you have to produce the number. For the whole exam, see what's on the SIE and how to study for the SIE exam.