Simple forward rates questions

[biboextreme]

I need some help with the following question:

If the forward rates at \(30/9/2015\) are as follows:

Year Rate
\(1\) \(-0.076\%\) (negative)
\(2\) \(-0.053\%\) (negative)
\(3\) \(\;0.020\%\)
\(4\) \( \;0.125\%\)

Then find the forward rate \(i\) for Year \(1\), but starting at \(1/01/2016\).

I tried working over two years: from \(30/9/2015\) to \(30/9/2017\)
\[
(1+(-0.076\%))^{1/4}(1+i)^{1}(1+(-0.0299947\%))^{3/4}=(1+(-0.053\%))^2\Rightarrow i=0.064536\%.
\]
I obtained the \(-0.0299947\%\) from the \(-0.076\%\) and \(-0.053\%\).

Thanks a lot!

 

[Muppet]

Unusual question. Assume we have to assume that rates are constant within each period - which seems to then contradict working out rates for overlapping periods.

Are those interest rates really %s? ie 0.076% and not 7.6%?

Anyway, if the rates given in the question are forward rates then I think you are using them incorrectly as spot rates. -0.053% is the 1-year forward rate from time 1??

So you could use
\[
(1+(-0.076\%))^{3/4}(1+(-0.053\%))^{1/4}=(1+ i)
\]