How to Derived Interest Rate from Bond Pricing Formula

[Jonaid]

Formula

P = FC ((1-(1-r)^-t )/ r) + (F / (1+r)^t)


I want to write this formula in terms of r = ??

Please help

 

[Ishuda]

Formula

P = FC ((1-(1-r)^-t )/ r) + (F / (1+r)^t)


I want to write this formula in terms of r = ??

Please help

An iterative approach should work for reasonable values of P, FC, and t. That is, let
s = (1+r)^t
and iterate on
r = ( FC (s-1) + F r ) / ( P s )
or possibly
r = FC (s - 1) / (P s - F)

No more than 4 or 5 iterations should be needed depending on wanted accuracy. A reasonable starting value for r might be .01

 

[Ishuda]

Your (1-r) on left should be (1+r) and your FC simply C; so:
...

You know, I completely missed that but when I wrote down the iterative equation I just assumed it was (1+r)^t

For your example we have the following iterates using the 2nd formula above:

0	0.01000
1	0.03707
2	0.06716
3	0.07756
4	0.07959
5	0.07993
6	0.07999
7	0.08000