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🧮 SIE guideUpdated November 20267 min read5 practice questions

SIE math formulas, with a worked example for each

The SIE is not a math test, but a handful of items need a quick calculation, and a calculator is provided (four-function at test centers, onscreen online). Here is every formula worth knowing, each with a worked example in round numbers. Examples are for exam practice only, not investment advice.

Bonds: prices and yields

FormulaExample
Bond price: 1 point = 1% of $1,000 par = $10A bond quoted at 101.5 costs $1,015
Basis point = 0.01%A yield up 50 basis points is up 0.50%
Current yield = annual interest ÷ market price5% coupon ($50 a year), price $950: 50 ÷ 950 = 5.26%

Price and yield move in opposite directions. For a bond bought at a discount: coupon < current yield < yield to maturity < yield to call. At a premium the order flips: coupon > current yield > yield to maturity > yield to call. Yield to maturity counts every coupon plus the gain or loss to par at maturity; yield to call does the same to the call date and call price.

Municipal bonds: tax-equivalent yield

Interest on most municipal bonds is exempt from federal income tax, so compare it with a taxable bond like this:

FormulaExample
Tax-equivalent yield = muni yield ÷ (1 − tax rate)3.5% muni, 30% bracket: 3.5 ÷ 0.70 = 5.0%
After-tax yield = taxable yield × (1 − tax rate)6% corporate, 30% bracket: 6 × 0.70 = 4.2%

The higher the tax bracket, the more the exemption is worth. Capital gains on munis are still taxable.

Mutual funds: NAV, offering price, sales charge

FormulaExample
NAV per share = (assets − liabilities) ÷ shares outstanding($52 million − $2 million) ÷ 4 million = $12.50
Sales charge % = (POP − NAV) ÷ POPPOP $10.60, NAV $10.00: 0.60 ÷ 10.60 = 5.66%
POP = NAV ÷ (1 − sales charge %)NAV $12.50, 5% charge: 12.50 ÷ 0.95 = $13.16

The sales charge is a percentage of the offering price, not of the NAV, which is why 0.60 is divided by 10.60. FINRA Rule 2341 caps the sales charge at 8.5% of the offering price. Redemptions are at NAV, less any deferred charge.

Options: breakeven, maximum gain and loss

One contract usually covers 100 shares; premiums are quoted per share.

PositionBreakevenMax gainMax loss
Buy 1 call, strike 50, premium 353Unlimited$300
Sell 1 call, strike 50, premium 353$300Unlimited
Buy 1 put, strike 50, premium 248$4,800$200
Sell 1 put, strike 50, premium 248$200$4,800

Calls: breakeven = strike + premium. Puts: breakeven = strike − premium. Intrinsic value is the amount in the money: with the stock at 56, a 50 call has 6 points of intrinsic value; if its premium is 7, the other 1 point is time value. Buyer and seller always mirror each other.

Margin

FormulaExample
Regulation T: deposit 50% of a margin equity purchaseBuy $20,000 of stock: deposit $10,000, borrow $10,000
Equity = long market value − debit balanceStock falls to $16,000: 16,000 − 10,000 = $6,000
FINRA maintenance (long): equity at least 25% of market value25% of $16,000 = $4,000; $6,000 is above it, so no call

FINRA Rule 4210 also requires at least $2,000 of equity in a margin account (though no one has to deposit more than the cost of the purchase).

Stocks and company numbers

FormulaExample
Dividend yield = annual dividends ÷ price$2 a year, stock at $50: 4%
EPS = (net income − preferred dividends) ÷ common shares($10M − $1M) ÷ 3M shares = $3.00
Current ratio = current assets ÷ current liabilities$6M ÷ $3M = 2
Working capital = current assets − current liabilities$6M − $3M = $3M
Conversion ratio = par ÷ conversion price$1,000 ÷ $40 = 25 shares
Parity stock price = bond price ÷ conversion ratioBond at $1,100 ÷ 25 = $44
Forward split: shares × ratio, price ÷ ratio2-for-1 on 100 shares at $60: 200 at $30
Real return ≈ nominal return − inflation6% return, 2% inflation: about 4%

A split or stock dividend changes the share count and price, not the total value.

✅ Test yourself: 5 questions

Four quick calculations; tap an answer to check it. Exam practice only, not investment advice.

Question 1 of 5

How does an investor in a zero-coupon bond earn a return?

  1. Buying below par, receiving par
  2. A dividend set by the board
  3. Monthly interest payments
  4. Interest paid at each call date
Show the answer and rationale

Answer: A

Zeros pay no periodic interest. They are bought at a deep discount and pay full face value at maturity; the difference is the interest earned.

📚 Learn it: Par, Coupon, Maturity: Reading a Bond

Question 2 of 5

All of the following are true of a bond trading at a discount EXCEPT:

  1. Its current yield exceeds the coupon
  2. Its YTM is below the coupon rate
  3. Its price is below par
  4. Its YTM exceeds its current yield
Show the answer and rationale

Answer: B

A discount bond's YTM is above its coupon, because the buyer also gains the discount at maturity. The other three statements are true of discount bonds.

📚 Learn it: The Price–Yield Seesaw

Question 3 of 5

A utility secures a bond issue with a lien on its power plants and land. The bonds are best described as:

  1. Mortgage bonds
  2. Collateral trust bonds
  3. Debentures
  4. Equipment trust certificates
Show the answer and rationale

Answer: A

Real property as collateral makes these mortgage bonds. Equipment trusts pledge movable equipment, and collateral trusts pledge securities.

📚 Learn it: Who Gets Paid First: Corporate Bonds

Question 4 of 5

After years of deflation, a TIPS's adjusted principal has fallen below its original principal at maturity. What does the investor receive?

  1. Nothing until CPI recovers
  2. The original principal
  3. Par plus a CPI bonus
  4. The lower adjusted principal
Show the answer and rationale

Answer: B

At maturity TIPS pay the greater of the inflation-adjusted principal or the original principal, so the original principal is a floor.

📚 Learn it: Bills, Notes, Bonds, TIPS and STRIPS

Question 5 of 5

Mortgage rates rise sharply. What is the main risk for an MBS investor?

  1. Currency risk
  2. Extension risk
  3. Call protection risk
  4. Prepayment risk
Show the answer and rationale

Answer: B

Higher rates discourage refinancing, so prepayments slow and the investor's principal stays tied up longer at the old, now-below-market rate.

📚 Learn it: Ginnie, Fannie, Freddie and the Mortgage Pool

Practice SIE calculations in the app →

Mixed practice with the math worked out in every rationale. No sign-up needed.

❓ Frequently asked

Is there a lot of math on the SIE?

No. A few items need a simple calculation, such as current yield, tax-equivalent yield, options breakeven, a fund's sales charge or margin equity.

Do you get a calculator on the SIE?

Yes: a four-function calculator at test centers and an onscreen calculator online. You cannot bring your own.

What is the formula for current yield?

Annual interest divided by the bond's current market price. A $50 coupon on a bond priced at $950 is a 5.26% current yield.

How do you calculate options breakeven?

For a call, strike plus premium; for a put, strike minus premium. The buyer and seller of the same option share the same breakeven.

How is a mutual fund sales charge calculated?

As a percent of the offering price: (POP − NAV) ÷ POP. FINRA caps it at 8.5% of the offering price.

📝 Practice this topic

📚 Learn it in the lessons

Sources

  1. FINRA, Understanding Bond Yield and Return (current yield, yield to maturity, yield to call, price vs yield)
  2. MSRB, Municipal Bond Basics (tax treatment of municipal bond interest)
  3. SEC, Mutual Funds and ETFs: A Guide for Investors (NAV, sales loads, breakpoints)
  4. FINRA Rule 2341, Investment Company Securities (8.5% maximum sales charge)
  5. SEC Office of Investor Education, Investor Bulletin: An Introduction to Options
  6. FINRA, Margin Regulation (Regulation T: up to 50% of the purchase price of a margin equity security)
  7. FINRA Rule 4210, Margin Requirements (25% maintenance on long positions, $2,000 minimum equity)
  8. FINRA, Prepare for Your Test Center Appointment: arrival, ID, calculator, note boards, breaks, results
  9. FINRA, Prepare for Your Online Test Appointment: check-in, ID, room scan, onscreen calculator and notepad, breaks

Checked November 2026. Rules in transition name their date; FINRA updates its exam pages and content outline from time to time, so check finra.org before you test. SIE is administered by FINRA; SIE Ready is not affiliated with or endorsed by FINRA. Exam preparation only, not investment advice.

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