Working out time period of government bond

Yes, another question!

September 2009 paper, Qu 1:

To answer this question, I found the value of i that solved the equation:

96(1 + i)^(182/365) = 100

I found i to be 0.085313


I then put this value of i into the equation:

97.89(1 + i)^(x/365) = 100

And solved it for x, to give x = 95. So 182 - 95 = 87 days.


However the solutions gave a completely different answer by using the fact that the investor received a rate of return of 5%, and solved the equation:

96(1.05)^t = 97.89

And found that t = 146 days.

I see why this answer works, but what's wrong with what I have done?

Thanks

 

But doesn't that conflict with what is in the notes?

P x (1 + i)^(n/365) = 100

That's the formula that's in the notes.

So on reconsideration, am I right to assume then that i is not a rate that is set by the specific bond, but more a by-product of the price it was purchased at, P, and the price at redemption, in this case £100? I thought i was associated with a government bill the same way D and c are associated with bonds.

Thanks

 

Yes the rate earned depends on 3 things, the price you buy it at, the price you redeem/sell and time in between. It is not set in stone.
It's not uncommon for holders of the same investments, eg bond, shares, over different periods, to earn different rates of return.

 

Ah ok thanks. I'd assumed that there is a bill that has a given i, and based on that you deduce how much you should pay for it. Almost as if you have a piece of paper with i written on it, and the price you sell it on for is dictated by the same i.

 

No, if you have a bill which would give you 3% to maturity and you need to sell it, and current buyers want 5%, you need to sell at the price corresponding to 5%, or hold onto it.

The coupons (bonds) and redemption amounts are written on the bond, but the price and hence value (and rate of return) are entirely dependant on what people are willing to buy or sell at.

 

Thanks!