Question 1086544
<font color="black" face="times" size="3">Problem 1


EAR = effective annual rate
EAR = (1+r/n)^n - 1
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We have some unknown interest rate. Call it x. This value is compounded quarterly to get some EAR, so,


EAR = (1+r/n)^n - 1
EAR = (1+x/4)^4 - 1
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We have another rate of 6% = 0.06 compounded semi-annually to get the same EAR value


EAR = (1+r/n)^n - 1
EAR = (1+0.06/2)^2 - 1
EAR = (1+0.03)^2 - 1
EAR = (1.03)^2 - 1
EAR = 1.0609 - 1
EAR = 0.0609
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Set the two EAR expressions equal to one another. Solve for x


(1+x/4)^4 - 1 = 0.0609
(1+x/4)^4 - 1+1 = 0.0609+1
(1+x/4)^4 = 1.0609
[(1+x/4)^4]^(1/4) = (1.0609)^(1/4)
1+x/4 = 1.01488915650922
1+x/4 - 1 = 1.01488915650922 - 1
x/4 = 0.01488915650922
4*(x/4) = 4*0.01488915650922
x = 0.05955662603689


which rounds to 0.0596 and converts to 5.96%


So if you have 5.96% compounded quarterly, then it's roughly equivalent to 6% compounded semi-annually.

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Problem 2


For each of these, we'll use the same formula as in problem 1
EAR = (1+r/n)^n - 1
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A)
r = 0.12
n = 4
EAR = (1+r/n)^n - 1
EAR = (1+0.12/4)^4 - 1
EAR = 0.12550881
EAR = 0.1255
EAR = 12.55%
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B)
r = 0.115
n = 12
EAR = (1+r/n)^n - 1
EAR = (1+0.115/12)^12 - 1
EAR = 0.12125932813801
EAR = 0.1213
EAR = 12.13%
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C)
r = 0.117
n = 2
EAR = (1+r/n)^n - 1
EAR = (1+0.117/2)^2 - 1
EAR = 0.12042225
EAR = 0.1204
EAR = 12.04%
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D)
r = 0.122
n = 1
EAR = (1+r/n)^n - 1
EAR = (1+0.122/1)^1 - 1
EAR = 0.122
EAR = 12.2%
Note: because of annual compounding, the EAR is the same as the nominal APR.
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The smallest EAR value is 12.04%, which is from choice C. That's why choice C is the answer. 
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Problem 3


EMR = effective monthly rate
EMR = EAR/12
12*EMR = EAR
EAR = 12*EMR


The EMR is given to be 1.2% = 0.012, so the EAR is,
EAR = 12*EMR
EAR = 12*(0.012)
EAR = 0.144
EAR = 14.4%</font>