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Find the nominal interest rate that, when compounded monthly, yields an effective interest rate of $6 \% /$ year.
Chapter 5
Exponential and Logarithmic Function
Section 3
Compound Interest
We need to find the nominal interest rate that is okay if the effective interest rate is 6. Okay, let's get this out of the way. Six per annum is what the effective is. Okay, let's get this out of the way. When it's compounded monthly. The total conversion period for a year is 12. It is possible to find out the arts. The formula for our effective is one plus R by am raised to the power m minus one. They're effective. We have less than 5%. The power 12 minus one can be written as 0.6 equals to one plus R by 12 raised to the power. We will add that both are patients by one. 1.6 equals to one plus R by 12 raised to the power 12. Okay, let's get this out of the way. We can take this one in the left hand side and it will go to one by 12 so 1.6 is raised to the power one by 12. Okay, let's get this out of the way. One plus R by 12 will be the result. Both are the questions by one, and now we will subscribe. 1.6 will be raised to the power one by 12 and two R by 12. To get the value of our, we will divide it by 12. We will add up 12 in this. It's so 12. It's going to be 1.06 raised to the power. Okay, let's get this out of the way. Uh will be good for 12 and 1.06 days to the government by 12. When we use a calculator, it will be 1.00484. Is there -1? We will be 12 by this. It will be zero It will be 0.0584 when we take 12 into account. Okay, let's get this out of the way. It is 5.84% in the city of Tampa. It's an approximate rate of interest. It's actually true. It is an approximation. Okay, let's get this out of the way. It will be approximately 5.84%. Thank you for that.
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