# Effective annual rate ear interest accrued at the end

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Effective annual rate (EAR)- interest accrued at the end of a year as a percentage of the principal amount o P x (1 + i)^number of periods, t = periodic interest rate o (Periodic interest rate – P)/ P = EAR APR doesn’t tell you how much you can expect to earn on each CD and therefore is not a good comparison, instead use the EAR o (1 + periodic rate) ^number of periods per year = 1 + EAR Pricing Securities Promising Multiple Payments T- bill = treasury bond Stripping- breaking up a security that promises multiples payments into constituent parts Market price of a coupon in m years: where C is equal annual coupon payments. im= market yield on m-year bills o C / (1 + im) ^m Present value, the market price, of a t-year bond with a face value of A and a coupon C is just the sum of the present values of the various payments, o P = (C + A) / (1 +it) ^t Bonds with a Coupon Period of Less than a Year Amortized Loans Amortized loan- security that promises a series of equal payments. Mostly home mortgages and automobile loans P = C / (1 + i) ^t. same equation as above A is just set to zero Annuity- amortized loan with annual payments o Annuity factor = C [ (1/i) x (1 – (1 / (1+ i^t))] Perpetuity- annuity that is payable forever, a bond that pays coupons forever, with payment of the face value deferred indefinitely o P = C/i this is because, the annuity factor includes the term 1 / (1 + i) ^t and as t gets large the value of this term approaches

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zero so the value of the expression in the square brackets approaches 1 / i Market Yield on a Security Promising Multiple Payments Yield to Maturity (YTM)- single interest rate at which the present value of a bond’s coupon and principal payments equals its market price o P = (C + A) / (1 + i) ^t solve for the value of i that satisfies this o The market yield on a bond is defined as the yield to maturity calculated from its market price o Approximate yield to maturity (AYTM) formula on page 77 Selling at a: o Discount= the market price of a bond is below its face value o Premium= the market price of a bond is above its face value o Par= bond is selling at exactly its face value Application: Understanding Treasury Listings Bonds: coupon security, have a maturity of over 10 years Notes: coupon security, a maturity of 2 to 10 years Bid price: price that dealers will pay for a security Asked price: Price at which dealers will sell a security

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