Approximation of interest rates.

Hello everyone, I had a doubt regarding approximation of interest rates. For example, while calculation gross redemption yield, in a given equation, we first approximate using two interest values and we then interpolate. What I want to know is, how to come to know those two interest values? In the notes, it is directly given as try 4% and 5% and then interpolate to get a value between 4 and 5 percent. Do we have to keep trying? Or is there a trick?

Thanks!

 

if there has any hint, then you can guess.
like, for finding APR whilst flat rate is given, then, The APR is roughly twice the flat rate.
or any suitable guess or keep on trying!

 

If there is no hint, I have to keep trying, right?

 

For Fixed Int Bonds start either start with a rate above or below(1-2% just to be sure) the coupon rate . Then you need to alter the rate depending on the effect it has on the price. If the price is higher than what's required, choose a lower rate, but if the price is lower than what''s required,then you need to increase your rate. If the first guess satisfies the equation, then you don't have to interpolate.But when you do interpolate just make sure that the interest rates you choose increase or decrease in steps of 0.005,i.e it's better to interpolate between 4 and 4.5% rather than 5%.

Hope this helped!

Kind regards
Sanjay

 

Why not use table function of your calculator instead of guessing.

Take this simple example

We've to find \(i\) such that

\( 13~ a_\overline{6|}^{(2)} + 100~v^6 = 120 \)
or
\( 13 \times \frac{1~ -~ (1+i)^{-6} }{2((1+i)^{0.5} - ~1) } + 100~(1+i)^{-6} = 120 \)

Now open Table MODE of your calculator and type

\( f(X) = 13 \times \frac{1~ -~ (1+X)^{-6} }{2((1+X)^{0.5} - ~1) } + 100~(1+X)^{-6} \)

START with 0.01

END - choose a big interest rate such as 0.2

STEP - 0.01

Now simply read the values

f(0.08) = 124.29
f(0.09) = 119.22

So interpolate between these two values.

 

Never knew about this "Table" function! Thanks a lot. Will try it out and let you know.

Thanks again. Cheers!

 

Hi all

Can't you just set up the equation of value and then use a financial calculator to determine the interest because this is possible for most of the problems I've come across. Or do you get penalised if you do not use interpolation to arrive at the yield?

Thanks in advance.

 

If you write down a correct answer with no indication of working you get full marks, but if it's wrong you get none. High risk strategy!

The only issue with using table functions for these problems (in my experience at least) is that frequently the function is too long to be input in your calculator.

 

Thanks Calum. I always substitute the yield I get back into the equation of value to confirm that it's the correct rate. I think maybe I should just make that part of my exam solution as well. What are table functions and what calculator has those? I have a Texas Instruments BA II Plus and a HP 12C Platinum but haven't seen anything like that. Thanks again.

 

My fx-85 does, at least.