Find the nominal rate which is compounded semi annually, yield an?

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S What is the nominal rate which is compounded semi annually, yields an effective rate?


a.4%


b.8%


c.10%


how to solve this, what are the possible solutions , thanks in advance

Find the nominal rate which is compounded semi annually, yield an?
The way to equate different compounding rates is to conduct a simple thought experiment: If I invested at a particular rate with a particular compounding, how much money would I have after one year.





With semi-annual compounding, I have (1 + semi-rate/2) after 1/2 year and (1 + semi-rate/2)^2 after one year. If I invest at the effective annual rate for one year, I get (1 + eff-rate) after one year. (That's the definition of the effective annual rate.)





Setting these two equations equal to each other, I get:





(1 + semi-rate/2)^2 = (1 + eff-rate) which implies that





semi-rate = 2*((1 + eff-rate)^0.5 - 1).





So a is 3.96%


And b is 7.85%


And c is 9.76%