### Current Yield

$$\text{Current Yield} = \frac{\text{Annual Coupon}}{\text{Current Price}} \times 100$$

**Where:**
- Annual Coupon = Face Value × Coupon Rate
- Price < Par → Current Yield > Coupon Rate
- Price > Par → Current Yield < Coupon Rate
- Price = Par → Current Yield = Coupon Rate

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### Approximate Yield to Maturity (AYTM)

$$\text{AYTM} = \frac{\text{Coupon} \pm \text{Price Change per Year}}{\text{Average Price}} \times 100$$

**Where:**

$$\text{Price Change per Year} = \frac{\text{Par Value} - \text{Purchase Price}}{\text{Years to Maturity}}$$

$$\text{Average Price} = \frac{\text{Purchase Price} + \text{Par Value}}{2}$$

> **Note:** Use **+** if bond is at a **discount** (price < par) — gain at maturity
> Use **−** if bond is at a **premium** (price > par) — loss at maturity

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### T-Bill Yield

$$\text{T-Bill Yield} = \frac{\text{Face Value} - \text{Purchase Price}}{\text{Purchase Price}} \times \frac{365}{\text{Days to Maturity}} \times 100$$

> T-Bills have no coupon — sold at a discount, mature at face value

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### Accrued Interest

$$\text{Accrued Interest} = \frac{\text{Annual Coupon}}{\text{Periods per Year}} \times \frac{\text{Days Since Last Coupon}}{\text{Days in Period}}$$

**Where:**
- Semi-annual bond: divide coupon by 2, use 182 days per period
- Annual bond: use full coupon, use 365 days per period

$$\text{Dirty Price} = \text{Clean Price} + \text{Accrued Interest}$$

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### Nominal Rate (Fisher Effect)

$$\text{Nominal Rate} = \text{Real Rate} + \text{Inflation Rate}$$

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### Present Value of a Bond (reference only — not calculated by hand)

$$PV = \frac{C}{(1+r)^1} + \frac{C}{(1+r)^2} + \cdots + \frac{C + FV}{(1+r)^n}$$

**Where:**
- $C$ = Coupon payment per period
- $r$ = Discount rate per period
- $n$ = Number of compounding periods
- $FV$ = Face value (par) received at maturity