Find the effective rate of interest corresponding to a nominal rate of 6%/year compounded annually, semiannually, quarterly, and monthly. (Round your answers to two decimal places.)
Okay i think i understand.
annually: 6%
semiannually: 6.09%
quarterly: 6.14%
monthly: 6.17%
Sure, let's break it down!
For nominal rate of 6% compounded annually:
The effective rate is also 6%.
For nominal rate of 6% compounded semiannually:
To calculate the effective rate, we need to divide the annual nominal rate by the number of compounding periods in a year, which in this case is 2 (since it's compounded semiannually).
So, the effective rate is 6% / 2 = 3%.
For nominal rate of 6% compounded quarterly:
Again, we divide the annual nominal rate by the number of compounding periods in a year, which is 4 (since it's compounded quarterly).
So, the effective rate is 6% / 4 = 1.5%.
For nominal rate of 6% compounded monthly:
Once again, we divide the annual nominal rate by the number of compounding periods in a year, which is 12 (since it's compounded monthly).
So, the effective rate is 6% / 12 = 0.5%.
Hope this helps, and remember: a little interest and a lot of humor can go a long way!
To find the effective rate of interest, we need to use the formula:
Effective Rate = (1 + (Nominal Rate / m)) ^ m - 1
where:
- Nominal Rate is the stated annual interest rate,
- m is the number of compounding periods per year.
Let's calculate the effective rate of interest for the given nominal rate of 6%/year compounded annually, semiannually, quarterly, and monthly.
1. Compounded Annually:
Here, m = 1 (compounded once a year).
Effective Rate = (1 + (6%/1)) ^ 1 - 1
Effective Rate = 1 + 0.06 - 1
Effective Rate = 0.06 or 6.00%
2. Compounded Semiannually:
Here, m = 2 (compounded twice a year).
Effective Rate = (1 + (6%/2)) ^ 2 - 1
Effective Rate = (1 + 0.03) ^ 2 - 1
Effective Rate = 1.0309 - 1
Effective Rate = 0.0309 or 3.09%
3. Compounded Quarterly:
Here, m = 4 (compounded four times a year).
Effective Rate = (1 + (6%/4)) ^ 4 - 1
Effective Rate = (1 + 0.015) ^ 4 - 1
Effective Rate = 1.0156 - 1
Effective Rate = 0.0156 or 1.56%
4. Compounded Monthly:
Here, m = 12 (compounded twelve times a year).
Effective Rate = (1 + (6%/12)) ^ 12 - 1
Effective Rate = (1 + 0.005) ^ 12 - 1
Effective Rate = 1.0617 - 1
Effective Rate = 0.0617 or 6.17%
Therefore, the effective rates of interest for the nominal rate of 6%/year compounded annually, semiannually, quarterly, and monthly are as follows:
- Compounded Annually: 6.00%
- Compounded Semiannually: 3.09%
- Compounded Quarterly: 1.56%
- Compounded Monthly: 6.17%
Do it the same way I just showed you in your previous post
http://www.jiskha.com/display.cgi?id=1304715894
Same type of question.
Just saw your other post.
What don't you understand?
I will do the quarterly rate problem.
Let the effective annual rate be i
so the interest factor will be (1+i)^1 for one year
(you should know the (1+i)^n part)
you want this to be equal to a rate of 6% per annum compounded quarterly , or
a rate of .06/4 or .015 per quarter, with n = 4
so (1+i)^1 = (1+.015)^4
1+i = 1.015^4
1+i = 1.06136551
i = .06136551
you wanted 2 decimals, so
the effective annual rate is 6.14 %
see if you can the others the same way.