Master the essential calculations for the RSE exam. Learn formulas for bond yields, margin calls, portfolio metrics, tax calculations, and financial ratios with step-by-step examples.
RSE Exam Math: What to Expect
You will not need complex multi-page calculus on the RSE exam. However, you will need to perform quick "napkin math" (like Margin Calls, Yields, and P/E ratios) and interpret what the numbers mean for a client.
Time Value of Money
Simple Interest
Formula: I = P × r × t
- P = Principal
- r = Annual interest rate
- t = Time in years
Used mostly for short-term instruments like T-Bills.
Compound Interest
Formula: FV = PV × (1+r)^n
This is why starting early is critical for retirement planning.
Rule of 72
Mental math shortcut to estimate years to double an investment.
Formula: 72 ÷ Interest Rate
Example: At 9% return, money doubles in approx. 8 years (72 ÷ 9).
Bond Calculations
Current Yield
Formula: Annual Coupon Payment ÷ Current Market Price
A snapshot of income - ignores capital gains/losses at maturity.
Duration Rule for Price Changes
Formula: Price Change ≈ -Duration × Change in Yield
Example: Duration = 7 years, rates rise 1% → Bond price drops approximately 7%.
Portfolio Metrics
Sharpe Ratio
Formula: (Portfolio Return - Risk Free Rate) ÷ Standard Deviation
Measures return per unit of Total Risk. Higher is better.
Treynor Ratio
Formula: (Portfolio Return - Risk Free Rate) ÷ Beta
Measures return per unit of Systematic (Market) Risk.
CAPM Formula
Formula: Expected Return = Risk Free Rate + Beta × (Market Return - Risk Free Rate)
Calculates the expected return required to justify the risk taken.
Margin Calculations
Margin Call Trigger Price
Formula: Loan Amount ÷ (1 - Maintenance Margin %)
Example:
- Buy $20,000 stock with $10,000 cash (50% margin)
- Loan = $10,000
- Maintenance margin = 30%
- Trigger Price = $10,000 ÷ (1 - 0.30) = $10,000 ÷ 0.70 = $14,285
Valuation Ratios
P/E Ratio
Formula: Market Price ÷ Earnings Per Share (EPS)
High P/E = High growth expectations. Low P/E = Value stock.
Dividend Yield
Formula: Annual Dividend per Share ÷ Current Stock Price
ROE (Return on Equity)
Formula: Net Income ÷ Shareholder Equity
The single most important measure of management efficiency.
Liquidity Ratios
Current Ratio
Formula: Current Assets ÷ Current Liabilities
Quick Ratio (Acid Test)
Formula: (Current Assets - Inventory) ÷ Current Liabilities
Excludes inventory because you can't pay bills with unsold stock in a crisis.
Tax Calculations
After-Tax Return
Formula: Return × (1 - Marginal Tax Rate)
Example: 5% GIC for client in 40% tax bracket = 5% × (1 - 0.40) = 3% after-tax.
Capital Gains
50% Inclusion Rate: Only half the gain is added to income.
Formula: (Proceeds - Selling Commissions) - Total Adjusted Cost Base (ACB)
Adjusted Cost Base (ACB)
Formula: Total Cost of all purchases ÷ Total number of shares
The weighted average cost including buying commissions.
Registered Account Limits
RRSP Contribution
Formula: 18% of previous year's Earned Income - Pension Adjustment (PA) + Unused Carry-forward
RESP Grant (CESG)
- 20% on first $2,500 contributed per child per year
- Max Annual Grant: $500 (or $1,000 catching up)
- Lifetime Max: $7,200 per child
T-Bill Yield
Formula: ((Par - Price) ÷ Price) × (365 ÷ Days to Maturity)
Since T-Bills don't pay coupons, the "yield" is the annualized capital gain.
Mutual Fund NAV
Formula: (Total Assets - Total Liabilities) ÷ Units Outstanding
The price of a mutual fund unit, calculated once daily at market close.
Sustainable Growth Rate
Formula: ROE × Retention Ratio
Where Retention Ratio = 1 - Payout Ratio
How fast a company can grow using only its own profits.
RSE Exam Tips for Math
- Memorize key formulas: Current Yield, P/E, Sharpe Ratio, Margin Call
- Rule of 72 is your friend for quick doubling calculations
- Capital Gains: Remember the 50% inclusion rate
- RRSP: 18% of earned income minus PA
- RESP CESG: 20% of $2,500 = $500 max annual grant
- Duration × Yield Change = Price Change (approximately)
- Always watch order of operations (BEDMAS)