The discussion revolves around calculating the effective interest rate per period for a loan with a nominal annual interest rate of 5% compounded semiannually. Participants are exploring how to interpret and apply this interest rate in the context of a loan repayment scenario.
Some participants have provided insights into the terminology used in finance, explaining the distinction between nominal and effective rates. There is an acknowledgment of the confusion surrounding these concepts, and the discussion is exploring the implications of these definitions without reaching a consensus.
Participants note that the textbook's explanation of the interest rates may not align with their understanding, leading to questions about the validity of dividing the nominal rate by two for semiannual compounding. There is also mention of the actual annual rate resulting from compounding, which adds to the complexity of the discussion.
ainster31 said:Homework Statement
I have borrowed $100. The interest rate is 5% per year compounded semiannually. How much will I have to pay the bank after 1 year?
Homework Equations
##F=P(1+i)^{ n }##, where i is the effective interest rate per period and n represents the number of periods
The Attempt at a Solution
How do I get the effective interest rate per period?
Curious3141 said:Shouldn't that just be the nominal annual rate (5%) divided by the number of compounding periods? What's the number of periods here?
ainster31 said:The textbook says that 5% interest every year compounded semiannually is the same as 2.5% interest every 6 months. But I don't understand how they're equivalent. How can you just divide by two?
Curious3141 said:Because this is apparently how economists and finance people think.
The 5% is called a 'nominal' *annual* rate. Dividing it by the number of compounding periods gives you an 'effective' *period* rate. Applying an exponential formula to it will give you the 'effective' *annual* rate.
That 5% quoted to you is actually a "fake" rate, meant to lull you into a false sense of security. The 2.5% every 6 months is a real thing, and it's simple to work out the actual compound interest you'll be paying at the end of the year. When you do the calculation, you'll find it's actually a little higher than 5%. That's basically how they pull the wool over your eyes when you take a loan without realising how much you'll actually end up owing. Of course, it works in your favour if you're actually investing and those are returns rather than a debt you're repaying.
You can look all this up easily on the web. It's just a matter of getting used to the (dumb) terminology.
ainster31 said:The textbook says that 5% interest every year compounded semiannually is the same as 2.5% interest every 6 months. But I don't understand how they're equivalent. How can you just divide by two?