[Verse 1] Sarah bought a corporate bond, ten thousand dollars paid Coupons come each year at six percent, plus principal repaid But when will all her money flow back into her hands? Macaulay's formula reveals the weighted timing plans [Chorus] Duration tells the story, weighted average time Cash flows multiplied by years, then divided by the price Present value weights each payment, early flows count less Macaulay duration measures bond's time-to-success [Verse 2] Take each coupon, take the face value coming at the end Discount back to present worth, that's where calculations blend Multiply each present value by its year number Divide by bond's current price, the magic you'll discover [Chorus] Duration tells the story, weighted average time Cash flows multiplied by years, then divided by the price Present value weights each payment, early flows count less Macaulay duration measures bond's time-to-success [Bridge] Longer maturity means higher duration Higher coupon rates create duration's reduction Zero coupon bonds show duration equals maturity Premium bonds have shortened time-sensitivity [Verse 3] If duration equals four-point-two, what does this convey? On average, four-point-two years till cash flows your way Not exactly when you'll break even on your spend But weighted time horizon that bond payments send [Chorus] Duration tells the story, weighted average time Cash flows multiplied by years, then divided by the price Present value weights each payment, early flows count less Macaulay duration measures bond's time-to-success [Outro] From first coupon to final payment, weighted by their worth Macaulay shows the balance point of cash flows on this Earth
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