Whilst at University, Oswald's aunt supported him financially. On 1 July 2012 Oswald agreed to pay her $10000 on 1 July 2017 and a further $10000 on 1 July 2022. At current rate of interest, the present value of these payments equal to $18762.47.

What is the duration of Oswald's liabilities to his aunt?

Question

Whilst at University, Oswald's aunt supported him financially. On 1 July 2012 Oswald agreed to pay her $10000 on 1 July 2017 and a further $10000 on 1 July 2022. At current rate of interest, the present value of these payments equal to $18762.47.

What is the duration of Oswald's liabilities to his aunt?

tkhunny · Answer

Third time I've seen this one.  Is no one teaching "Basic Principles" out there?

$10000v^5 + $10000v^10 = $18762.4

Can you solve for v?

anonymous · Answer

how do i find duration in years after found i? thx

tkhunny · Answer

You'll need a definition of "Duration".  Do you have one?  Please share.

anonymous · Answer

Definition of Duration: For some holding period the rise in price is exactly offset by the decrease in return from the reinvested coupons ,
This special holding period is known as the Duration of the bond 

So how can i work out thx

tkhunny · Answer

Well, okay, there is some ambiguity, here.  It is the nature of the word "Duration".  You have supplied the defintion of "Modified Duration".  For this definition of "Duration", we'll have to decide on what "Unit Change" to use for the interest rate.

Gererally, 1% is a very large change.  Why not use 1 Basis Point, or 1% of 1%.

Once you solve this for i, $10000v^5 + $10000v^10 = $18762.4, calculate the new price using i + 0.0001 and see what happens.  You may also want to calculate with i - 0.0001 to check for symmetry.

Sound like a plan?

anonymous · Answer

quite make sense    im working on it

anonymous · Answer

The i is 0.00858355 that I cal

SO using the  hint u told me  I figure out the D =8.6667 years


I cant desire to ask u the final answer
but its make sense? 
thx so much!

tkhunny · Answer

Well, there's that ambiguity again.  The "Duration" you have defined is NOT measured in years.  If you want to calculate a "McCauley Duration", you can report it in years.

anonymous · Answer

I actually calculator by finding Pi1 and Pi0 

Using the MD = D/(1+i)

I think I got it 

thanks again!

tkhunny · Answer

Fair enough.  Any time anyone just says "Duration", don't let them get away with it.  Make them tell you what they mean.

anonymous · Answer

I pretty sure for this Question. 

I was wondering if u could help me with the one  Floting rate bond Question?

Its quite urgeny  pls help

anonymous · Answer

Once again thx!