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Implicit yearly interest rate

 
 
Reply Fri 28 Oct, 2016 10:23 am
Hello, I have a question regarding computing an implicit yearly interest rate of choice. We got ten questions and each question had 2 options (we chose 1 option), for instance:
a)Which alternative do you prefer?
1- 1000 euros now
2- 1040 euros in two months

b) Which alternative do you prefer?
1- 1000 euros now
2-1080 euros in two months

And we have to compute the implicit yearly interest rate of choice (for each question). We should use the formula r= -1 + root(T)(M/C) ...T=time in years, M=final capital, C=initial capital and r=interest rate.
However, my results are still wrong and weird, it makes me confused that in option there are months but in formula year and we have to calculate yearly implicit interest rate. Would anyone know how to compute, please?

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engineer
 
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Reply Fri 28 Oct, 2016 11:06 am
@barbara111,
Your formula is definitely wrong. You can get a rough yearly rate using

r = (-1 + M/C) / T

For your first example (-1 + 1040/1000) / (2/12) = 24%

A more exact rate is r = (-1 + M/C) ^ (1/T)

(-1 + 1040/1000) ^ (12/2) = 26.5%
engineer
 
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Reply Fri 28 Oct, 2016 01:01 pm
@engineer,
A correction, your formula is correct, I read it wrong.

Mine should be -1 + (M/C)^(1/T). When you write -1 + root T (M/C) I'm guessing you mean the same thing. The "root T" threw me, sorry.

Still, -1 + (1040/1000) ^ (12/2) = 26.5%
barbara111
 
  1  
Reply Sat 29 Oct, 2016 08:10 am
@engineer,
OK, it seems that makes sense. So I can express the months in the way that instead of 1/T I will compute 12/1? As I am not sure, what exactly the number 1 symbolizes. Anyway, thank you!
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