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The following question is about how the effective annual rate (EAR) changes with different compounding frequencies. For a nominal annual rate or APR of 6%,
The following question is about how the effective annual rate (EAR) changes with different compounding frequencies. For a nominal annual rate or APR of 6%, give the EAR for the given number of compounding periods, m. The EAR with quarterly compounding, i.e. m=4, is %. (Round to two decimal places.) The EAR with monthly compounding, i.e. m=12, is %. (Round to two decimal places.) The EAR with daily compounding, i.e. m=365, is %. (Round to three decimal places.) The EAR with hourly compounding, i.e. m=8,760, is %. (Round to three decimal places. Be careful not to round your hourly rate too much while doing the calculation, since it will be very, very small.) Now, look for a pattern in your answers. What happens to the effective annual rate (the EAR) as the number of compoundings per year, m, increases? A. The EAR increases at an increasing rate (i.e. the increase in EAR gets bigger and bigger). B. There is no clear pattern - sometimes the EAR goes up, other times it goes down. C. The EAR decreases. D. The EAR increases at a decreasing rate (i.e. the increase in EAR gets smaller and smaller). Given the observed patterns in EAR as m increases (and given the discussion of this subject in the slides/lectures), is it plausible that an APR of 6% would lead to an EAR of, say, 7% or 8% or even 16% if m gets sufficiently large? A. No, those rates are not plausible. More frequent compounding always increases the EAR, but the marginal effect gets smaller and smaller, so you cannot get that large an increase in EAR merely by increasing m. B. Yes, we can see that EAR increases when m increases, so any EAR is plausible for a sufficiently large m
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