The EAR converts a stated annual percentage rate to a rate that indicates the actual amount of interest paid when the frequency of compounding is accounted for. If a stated APR is 6.0302 percent, compounded monthly, then the EAR is found by dividing the APR by 12 months – 0.060302/12 = 0.00502517; adding 1 – 1.00502517 – and finding the 12 power (^12) of the sum – 1.00502517^12 = 1.062; and subtracting 1 – 1.062 - 1. The EAR for this example is 6.20 percent.

If a Treasury Bill (a discount bond with par value of $10,000) can be bought for $9,950.00, and has 30 days left to maturity, the BEY is calculated by first dividing the par value by the price and subtracting 1 – $10,000/$9,950.00 - 1 – to arrive at a 0.005025, or 0.5025 percent, growth in value over 30 days. Multiplying this growth by the number of 30-day periods in a year (365 days per year divided by 30 days left to maturity) – 0.005025 x (365/30) – results in a BEY for this example of 6.11 percent.

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A: Lets look at an example. Assume a $1000 face value bond, semi-annual 8% coupon bond 20-year bond. First let’s calculate the semi annual YTM: FV = 1,000, PV = -950, N= 40 and PMT = 40. Solving for *i* we get 4.26%. This is the semi-annual YTM. Simply multiply by 2 to get the BEY or 4.26% x 2 = 8.52%. Now we can calculate the EAR as (1+.0852/2)^{2} -1 =.0870or 8.70%.

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