# AdditionalEFFProblem - Now calculate the value of the first...

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You have just bought a security that pays \$500 every six months. The security lasts for 10 years. Another security of equal risk also has a maturity of 10 years, and pays 10 percent compounded monthly (that is, the nominal rate is 10 percent). What should be the price of the security that you just purchased? a. \$6,108.46 b. \$6,175.82 c. \$6,231.11 d. \$6,566.21 Step 1: Find the appropriate discount rate. m NOM 1 EFF = (1+ ) m + 12 .1 1 EFF = (1+ ) 12 + 1 + EFF = 1.1047 EFF = 10.47% Or, using a financial calculator: P/YR = 12; NOM% = 10; and then solve for EFF% = 10.4713%. Then, convert this effective rate to a semiannual rate: m NOM 1 EFF = (1+ ) m + 2 NOM 1 .1047 = (1+ ) 2 + Raise each side of the equation to the ½ or .5 power, and solve for NOM = 10.2%. EFF% = 10.4713; P/YR = 2; NOM% = 10.2107%.
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Unformatted text preview: Now, calculate the value of the first security as follows: N = 10 × 2 = 20; I = 10.2107/2 = 5.1054; PMT = 500; FV = 0; and then solve for PV = -\$6,175.82. Note that 10% compounded monthly is really 10.47%. 10.21% compounded semi annually is also really 10.47%. This is the only way that you can compare rates with different compounding periods. Note also that you can’t take a short cut – you can’t say, well let’s just calculate 10% compounded semi annually (which is (1.05) 2 – 1 = 10.25%. While this is close to 10.21%, using 10.25% s the discount rate will not give you the correct answer; it will just give you an approximately correct answer....
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