What is the appropriate stated annual interest rate for the following?

If The effective monthly interest rate is 5%, then match each of the following compounding frequencies with its appropriate stated annual interest rate:





Annual compounding


Quarterly compounding


Monthly compounding


Daily compounding





58.9%


68.0%


58.6%


60.0%


64.7%


63.1%


79.6%





Wouldn't they all be 60.0% if we are looking for the STATED annual interest rate? In other words, for the stated rate, it shouldn't matter what the compounding frequency is.|||First, we need to convert the effective MONTHLY rate of 5% to an effective ANNUAL rate. Let i = effective annual rate. We need to solve the following formula for i:





1 + i = (1.05)^12


i = .7959, or about 79.6%.





Thus, the effective annual rate is 79.6%





I assume that "stated annual rate" is the same thing as "nominal interest rate".





To find the stated annual rate, we will solve the following formula for i^(m):





i^(m) = m * [(1 + i)^(1/m) - 1] where





i^(m) is the stated rate compounded m times per year


i is the effective annual rate, expressed in decimal form








1. annual compounding





This is the same thing as the effective annual rate. Therefore, i^(1) = 79.6%.





2. quarterly compounding





i^(4) = 4 * [1.7959^(1/4) - 1] = .6305, or 63.1%





3. monthly compounding





i^(12) = 12* [1.7959^(1/12) - 1] = .6, or 60%





We could have also solved the following formula for i^(m):


i^(m)/m = j, where





i^(m) is the stated rate compounded m times per year


j is the effective rate for 1/m of a year





i^(12)/12 = .05


i^(12) = .6, or 60%





4. daily compounding





i^(365) = 365 * [1.7959^(1/365) - 1] = .586, or 58.6%|||You didn't bother to vote for me, so I had to waste time voting for myself. I am blocking you so that I remember not to answer any more of your questions. Maybe you'll then learn to show a little more appreciation.

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