Can anyone please explain how to use the calculator to find continous compunding? Its mannual doesn’t explain what inputs I need to put.
Here is the question that is from CFAI:
Q: For liquidity purpose, a client keeps $100,000 in a bank account. The bank qoutes a stated annual interest rate 7 percent. The bank’s service representative expains that the stated rate is the rate one would earn if one were to cash out rather than invest the interest payments. How much will your client have in his account at the end of one year, assuming no additions or wthdrawals?
So far what I did was with the calculator:
PV = -100,000
and then I don’t know what to do. The answer based on the book is $107,250.82
For continuous compounding you need to use the exponential function: e^x. (Think of the “x” as a superscript; I can’t do an actual superscript in my post here.)
So:
7%, e^x, gives 1.0725082
× 100,000, gives 107,250.82.
That’s it.
To do the reverse – to get the continuously compounded rate – you use ln(x) (it might be capitalized: LN(x)).
If $100,000 grows to $105,000 in one year, what’s the continuously compounded rate?
I do it a rough way. Go to P/Y, put in whatever, 1,000,000 periods (I figured that’s close enough to continuous)
Then you type 1 for year, then 2nd “N”, and it will also do 1,000,000 periods.
Then solve as usual.
I think schweser recommends you DO NOT change P/Y, because if you do, you better change it back for the next problem. But that’s how I figured out how to do it.
To change between nominal to continuous, there is a fuction called ICONV, you force the calculator to do a very large number of periods and it does the same thing. I don’t remember how, look in the manual to practice.
In case you want to know what’s happening behind the curtain:
The continuously compounded rate is simply the limit of the function x = (1 + (r/n))^n as n goes to infinity. Think of how the effective annual rate for 10% changes as you go from annual to semi-annual to quarterly to monthly compounding. Going from annual to semiannual makes a big difference - from 10% to 10.25%. Going from semiannual to quarterly makes a smaller difference - from 10.25% to 10.38%. So, the change as you go to a higher frequency tails off. Once you get to about 1,000 periods a year, you etremely close to the continuously compounded value.
