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Compound Interest and Effective Interest rates are the same things?
We will calculate effective interest rate only when we have interest which is compounded either semi-annually, quarterly, monthly or daily using the formula given for compound interest (that is why you don’t mention another formula for the effective interest in your notes).
We calculate Effective interest rate to know that what is our actual rate of return or pay (depend whether we have made investment or borrowing) which will be greater than nominal interest rate because we have interest compounded quarterly or daily.
For Example:
If we have deposited $10,000 in the Bank where we will receive 8% p.a. compounded quarterly. What is the interest we receive after one year.Answer:
P(1 + r)^n
$10,000(1 + 0.02)^4 = $10,824.32or we can calculate with this formula which result in exactly the same answer
P(1 + r/n)^n
$10,000(1 + 0.08/4)^4 = $10,824.32Please correct me if wrong anywhere!
I know that it might not be relevant to the topic directly but it does confuse me that is why I asked you. I appreciate your answer! Thank you 🙂
You are correct. In your first answer you are using r as being the 3 monthly interest rate and in your second answer your are using r as being the annual rate which is why both answers are exactly the same.
When compounding you always multiply by 1 + the period interest rate (in this case the 3 month rate) to the power of the number of period (in this case 4 periods of 3 months).
What I have said about compound interest & effective interest is the same thing along with the information about the effective interest that I asked before the given example is also correct?
Thanks for your answer sir. That means a lot 🙂
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