The thing is that I always use EAR and If I do I get a rate that is above 8…
maybe I´m using a formula that I shouldn`t…
I found another one in the book
FVn = PVersN
I don`t think this formual is easy to remember through, I always gets confused with this e in my calculator (I read the manual of the hp12c that says that)
from the manual:
Natural antilogarithm. Raises and (approximately 2,718281828) to the power of the number shown in record X
But I need to get that number e raised over 11*0,08 not the 11*0,08 raised to e…
I get so confused when I have calculations involving e
for the BA2 plus, and maybe the HP calculator, you need to type the exponent first,
and then hit 2nd -> ex
this is different from the TI-30XS, and most non-financial calculators, where you first type ex and then the exponent.
knowing how to find the effective rate of interest given a nominal rate with arbitrary number of compounding is fundamental. incidentally, continuously compounded is just like regular compounding, but the number of times the interest rate is compounded is infinity. this is why you can approximate the effective rate the way i suggested in a previous post, by making the number of compounding large enough.
the ex formula you may have in your notes comes from taking the limit of the compounding formula.
This makes more sense, I guess I will need to know the formula + the ex that is inversed, typing the exponent first.
I really hate this continuous compounding thing but Im getting better with it over the time (I dont see how continuous compounding is usefull in real life, I never see a bond that changes value (due to the rate changing) in the same day, maybe theres something like that in Fixed Income but I still dont got to this content.
I clearly understand what they`re, the exercise gives me a Effective Annual Rate and I need to transform it on a Stated Annual Rate (so if I do it the stated needs to be lower the value of effective), my problem is the continuous compounding thing.
The best way for me would find what would be the nominal rate compounded annual, but the exercise gives me compounded continuous, how can I convert the continuous to annual?
A nominal rate compounded annually is an effective annual rate. You’re correct: that’s what you want.
The continuously compounded rate is 8%. This is a nominal rate; i.e., at the end of one year the value of your investment will not have increased by exactly 8%.
To convert from a continuously compounded rate (rcc) of 8% to an effective annual rate (EAR), use:
There’s the problem: they _ don’t _ give you an effective annual rate. They give you a nominal (or stated), continuously compounded rate.
An effective _ annual _ rate compounds _ annually _, not semiannually, not monthly, not daily, not continuously.
No, you don’t.
When using the TVM buttons on your calculator, i is always – _ always! _ – an effective rate, not a stated rate. And it is always – _ always! _ – the effective rate for one (payment) period.
Here, you’re given a stated (continuously compounded) rate, so you need to convert it to an effective rate. And, because you want to measure time in years (you’re using n = 11 (years)), you want to convert it to an effective _ annual _ rate.
I found this topic really hard because in some situations as this the exercise gives the stated anual rate, compounded continuosly.
Some other questions gives like: A bank compounds interest continuosly on its deposit and offers an effective annual interest rate of 14%, than it asks what is the annual interest rate.
^ So the bank says it offers an EAR of 14% and you have to solve for the nominal annual rate:
1 +0.14 = er where r is the nominal annual rate, compounded continuously
ln (1.14) = ln [er]
r = ln (1.14)
r = 0.131028262
There is an ICONV worksheet on the BAII which lets you enter EAR, nominal rate and compounding frequency. If I use frequency = 525,600, EAR =14, I get a NOM of 13.10282787, which is pretty darned close to the actual answer.
