SERVING THE QUANTITATIVE FINANCE COMMUNITY

rahu
Topic Author
Posts: 3
Joined: October 1st, 2008, 8:07 am

### Newbie question on cont. compounding

"A rate of 6% per annual with cont. compounding translate into 6.09% with semiannual compounding". How the figure 6.09% comes from 6%? Can anyone explain pls?

Fermion
Posts: 4486
Joined: November 14th, 2002, 8:50 pm

### Newbie question on cont. compounding

QuoteOriginally posted by: rahu"A rate of 6% per annual with cont. compounding translate into 6.09% with semiannual compounding". How the figure 6.09% comes from 6%? Can anyone explain pls?You need to understand the difference between continuous compounding and semi-annual compounding. Once you do, then it is easy to work out for yourself what the equivalent rates are. If you don't understand this difference, then you need to ask your teacher. They need to know that you don't know.

gjlipman
Posts: 1102
Joined: May 20th, 2002, 9:13 pm

### Newbie question on cont. compounding

If you invest $1 at 6% continuously compounding, at the end of the year you will have e^(0.06)=1.0618.If you invest$1 at x semiannual, at the end of the year you will have (1+x/2)^2.So, x=2[sqrt(1.0618)-1]=6.09%.

Anthis
Posts: 4313
Joined: October 22nd, 2001, 10:06 am

### Newbie question on cont. compounding

I second Fermion's words of wisdom. Just to help you a bit, in such problems you will always have 2 out of three parameters(the initial value level, the end of horizon T value level and a capital growth rate or interest rate) and a compounding condition. Compounding is the process where accrued interest is capitalised and next periods' interest is estimated upon this amount too. The frequency this process is iterated is expressed in the compounding condition. It can be annual semi-annual, quarterly, monthly, weekly, daily even continuous In the later the compounding process is iterated every nanosecond virtually.The higher the compounding frequency, the lower the interest rate. Morever this difference is more pronounced for longer investment horizons.For better digesting of the above solve the problem below:1) You are offered to buy today for $95 a bond that pays back to you$100 in a year. Whats the rate of return for your investment of \$95 (yield to maturity) if the compounding is: a)annual, b)quarterly, c) monthly and d) continuous?

Vegawizard
Posts: 157
Joined: November 27th, 2006, 10:46 am

### Newbie question on cont. compounding

QuoteThe higher the compounding frequency, the lower the interest rateAnthis, while I would second your advice, may I suggest that your above statement could be ambiguous:If a stated interest rate (simple interest) is quoted at 10%, then the more frequently you compound this rate, the higher the effective rate is, 10% becomes 10.25% effective with semi-annual compounding and 10.38% with Quarterly compounding.When you have discreet PV & FV, and are solving for the rate of return, then the more frequently you compound, the lower the nominal rate.

Anthis
Posts: 4313
Joined: October 22nd, 2001, 10:06 am

### Newbie question on cont. compounding

Your point is valid but since rahu seems to be a beginer i refrained to confuse her with the various flavours of rates (eg effective rate). I tried to direct her think in terms of a triangle initial value, terminal value, and rate (interest or growth rate), given a compounding condition. In this setting given a compounding condition, we must have the two out of the three elements of the triangle.In the example you presented, you have implied an initial value, a base interest rate and you try to find the effective interest rate (and terminal value) for various, not given, compounding conditions.HTH