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Working out time period of government bond

M

maz1987

Member
Yes, another question!

September 2009 paper, Qu 1:

A 182-day government bill, redeeable at £100, was purchased for £96 at the time of issue and was later sold to another investor for £97.89. The rate of return received by the initial purchaser was 5% pa effective.

(a) Calculate the length of time, in days, for which the initial purchaser held the bill
Click to expand...

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
 
maz1987 said:
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.

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


  1. You didn't use the rate given in the question for the first investor
  2. You then assumed the second investor also received this incorrect rate
 
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
 
Last edited by a moderator:
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.
 
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