Converting interest rates

[Remofiloe]

I know it may be a bit daft, but i keep getting confused when i have to convert pthly effective rates to an annual rate, can somebody help out.

Is there anybody out there?

 

[Newcomer101]

Hi Remofiloe,
(apologies- there seems to be no nice way of writing formula)

i^(p)=p[(1+i)^(1/p)-1]

i^(p) is the pthly effective rate. If you sub in your values for p and i^(p), then you can rearrange to find i (which is the annual effective rate).

Hope this makes sense.

----------------------------------------------------

Sorry...just re-read what I wrote and realised its incorrect (i^(p) is the nominal effective rate convertible pthly) and that it doesn't even answer your query. I wrote it dead quick- this will be my downfall in the exam

 

[Remofiloe]

Hi Remofiloe,
(apologies- there seems to be no nice way of writing formula)

i^(p)=p[(1+i)^(1/p)-1]

i^(p) is the pthly effective rate. If you sub in your values for p and i^(p), then you can rearrange to find i (which is the annual effective rate).

Hope this makes sense.

Hi and thanx a bunch for responding, that bit i get, the problem comes when a question requires me to match interest rates to the term, like maybe calculating interest per annum, when you are given a quarterly rate.

 

[Remofiloe]

Hi and thanx a bunch for responding, that bit i get, the problem comes when a question requires me to match interest rates to the term, like maybe calculating interest per annum, when you are given a quarterly rate.

. i mean it doesnt look like its a simple matter of multiplying by the time period, i dont get an accurate answer when i do that.

 

[Eulero]

The important thing to know is that there are nominal per annum quarterly rates, they are basically just listed to make finding the effective quarterly rate really easy i.e. nominal rate per annum divided by 4.

If you already have the effective quarterly rate j then we have the accumulation for 1 year of:

(1+j)^(4)

If you want to find the annual effective rate from that simple (1+j)^4 has to be equivalent to a one year accumulation done once, so (1+i) = (1+j)^(4)
and then solve from there.

 

[tiger]

Hi Remofiloe,
I found the notes a little confusing also when I first studied this.
The thing to realise is for example, if interest is quarterly then we can say the period is 0.25 or there are 4 periods per year. The formulas will be slightly different either way.
From what I remember the notes sometimes uses letters like n for the fractions, where as in my mind n is normally an integer.

Sorry don't have the notes to hand so can't give a specific example.
Hope this helps.

 

[Remofiloe]

Thanx a buch

you guys

 

[hatton02]

I'm also struggling with these. If it mentions nominal rates I think I'm OK as I just use i to the (p) and get i from that. The thing I struggle with is if they say "convertible quarterly" or something.

If an interest rate is 8% pa convertible quarterly, how do you work out i (i.e. the interest rate per annum). How do you work out i (i.e. the interest rate per quarter or however it's phrased)?

Sometimes I see them just say "8% pa convertible quarterly is the same as 2% effective pa quarterly rate" but then other examples in the answers they seem to do like (1+something)^p -1 and then other times they do something else. It's so confusing. Why can you just divide 8 by 4 to get 2 and other times you can't? I can't believe how important it is to understand this to answer all the questions yet the introduction to this is poorly explained and seemingly skipped over as if it's not important or is easy!

Any help converting these would be appreciated.

Thanks.

Edit: Found it in the notes. The solution to 6.8 confused me so much numerous times. The main things I circled were: "An interest rate of 8% pa convertible quarterly is equivalent to an effective quarterly rate of 2%". Now I'm trying to learn this as "it says per annum which is 12 months and we want 3 months so divide by 4, fine" but then later it says: "Alternatively, you could have worked in months using an effective monthly interest rate." So I'm thinking, OK, 2% for 3 months, so for 1 month it's just 0.666% right? Wrong...apparently it's 0.66227%. Where's the logic in this? Please help! It's killing me.

 

[niroshmonster]

Equivalent rates

Hi
You should get a book called corporate finance demystified ........ its like CT1 for dummies. You are not alone in your battles with it. Mail me.
Nirosh Monster

 

[bobbathejobba]

Hi
You should get a book called corporate finance demystified ........ its like CT1 for dummies.

Nah - it's more of a CT2 book than CT1. Though it does give a good overview - but just not enough detail to really be helpful...

 

[John Lee]

but then later it says: "Alternatively, you could have worked in months using an effective monthly interest rate." So I'm thinking, OK, 2% for 3 months, so for 1 month it's just 0.666% right? Wrong...apparently it's 0.66227%. Where's the logic in this? Please help! It's killing me.

When working with effective rates you need to use powers.

So 2% effective per 3 months is equivalent to 1.02^(1/3) = 1.00662271.

ie 0.662271% per month.

Or if you prefer we're equating the accumulation factors:

Accumulation factor for 3 months using the 3 monthly effective rate is 1.02.
Accumulation factor for 3 months using the 1 month effective rate is (1+i)³.

Hence (1+i)³ = 1.02 so i = 1.02^(1/3).

Whereas convertible rates aren't proper rates - they're expressed as annual rates but they're not really. So you have to first swap them to effective rates first either by using i(p)/p to give the pthly effective rate or using the (1+i) = (1 + i(p)/p)^p to get the annual efffective rate.

If it helps I have rewritten the Core Reading for chapter 2&3 so it's a bit more clear drop me an email if you want it. Hopefully the Profession will take this on board so it is clearer.

 

[suryamani]

Hi

When working with effective rates you need to use powers.

So 2% effective per 3 months is equivalent to 1.02^(1/3) = 1.00662271.

ie 0.662271% per month.

Or if you prefer we're equating the accumulation factors:

Accumulation factor for 3 months using the 3 monthly effective rate is 1.02.
Accumulation factor for 3 months using the 1 month effective rate is (1+i)³.

Hence (1+i)³ = 1.02 so i = 1.02^(1/3).

Whereas convertible rates aren't proper rates - they're expressed as annual rates but they're not really. So you have to first swap them to effective rates first either by using i(p)/p to give the pthly effective rate or using the (1+i) = (1 + i(p)/p)^p to get the annual efffective rate.

If it helps I have rewritten the Core Reading for chapter 2&3 so it's a bit more clear drop me an email if you want it. Hopefully the Profession will take this on board so it is clearer.

Just to say the same thing in a different way: Nominal rate may be expressed as annual rates, but may not be calculated annually... these are calculated p times in a year.. so 8% pa convertible quarterly is the same as 2% being calculated every quarterly.. but effective annual rate for this would be (1.02)^4 - 1 = 8.243 %.

 

[Calum]

Nothing to be ashamed of. It is one of those oddities that is rarely of practical use (that I have seen, anyway).

To get from i(12) to i:

1) Divide i(12) by 12
2) Add one
3) raise to the power of twelve.
4) You now have 1+i.

So, for example, i(12) = 0.048889

1) 0.048889/12 = 0.004074083
2) 1+ 0.004074083 = 1.004074083
3) 1.004074083^12 = 1.05
4) i=5%