risk discount rate payble continously

In recent exam to calculate the forward price of the contract, it was provided that the risk discount rate is 5.00% PA payble continously, what does it mean?

 

Surely i = exp(0.05) - 1 ??

 

Hope the attached word file may enhance the concept of discount rate payable continuously.

 

Your have calculated by the force of interest, But in th exam it was clearly stated that,
risk discount rate payble continously

 

Without any further information, I'd assume that "risk discount rate is 5.00% PA payble continously" means the effective interest rate is 5% and it needs to be converted to a force of interest. But it is unclear and I'd be surprised if you weren't credited with eitehr assumption provided you were clear about what you took it to mean.

 

Does not it mean that "effective rate of interest 5% pa payable continuously" is same as "force rate of interest 5% pa"?
Please elaborate the concept.

 

You're overcomplicating things. If you are given a continuously compounded interest rate "r" then all you need to use is e^-rT to discount, where T is the number of years (nice and easy if it's 1 year).

Hobbs and asmkdas are right, you can calculate the effective annual rate using i = e^r - 1, but what's the point? That's not what the question asked.

 

The "effective rate of interest" is assuming one interest payment at the end of the year.
The question implies that the interest is actually paid continuously, which will be at some force of interest delta.

delta = ln(1+i) = 0.04879,

So if the interest is being paid continuously, it is being paid at a force of 4.9%. This will result in the same accumulation as an annual interest payment at 5%.

 

As far as I know the "effective interest rate of 5% p.a. payable continuously" does mean that "the force of the interest rate is 5% p.a" means delta=0.05
Please explain if I've the wrong concept.

 

The point is that "effective rate of interest" refers to interest that is paid periodically, not continuously. Therefore, adding the word continuous to that phrase makes it unclear what the 5% figure means. Does it mean that delta is such that it is equivalent to a 5% effective rate, or does it mean delta actually is 5%?