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Q9 september 2009

S

Szery

Member
Q9 september 2011

I don't understand how PV is calculated.

T spot effective rate for consecutive years rates are y(t) = 0.02 0.04 0.06 0.08 0.1

Valuation rate of interest are a(t)=0.031 0.052 0.073 0.094 0.115

So PV in mind mind should be
PV= 100 (1+a(5))/(1+y(t))^5 +10*sum (1+a(k))/(1+y(k))^k

but it is not the case because PV factors in the solution differ.

Thx for any help
 
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Szery said:
I don't understand how PV is calculated.

T spot effective rate for consecutive years rates are y(t) = 0.02 0.04 0.06 0.08 0.1

Valuation rate of interest are a(t)=0.031 0.052 0.073 0.094 0.115

So PV in mind mind should be
PV= 100 (1+a(5))/(1+y(t))^5 +10*sum (1+a(k))/(1+y(k))^k

but it is not the case because PV factors in the solution differ.

Thx for any help
Click to expand...

Is this for the IAI exam - as the S09 Q9 is about stochastic interest rates...
 
Szery said:
I don't understand how PV is calculated.

T spot effective rate for consecutive years rates are y(t) = 0.02 0.04 0.06 0.08 0.1

Valuation rate of interest are a(t)=0.031 0.052 0.073 0.094 0.115

So PV in mind mind should be
PV= 100 (1+a(5))/(1+y(t))^5 +10*sum (1+a(k))/(1+y(k))^k

but it is not the case because PV factors in the solution differ.

Thx for any help
Click to expand...

The a(t) in your formulae are the spot rates you should using to discount not the y(t).
 
In part (ii), I assume.

You calculate the PV by taking each cashflow and discounting it accordingly using the relevant interest rate. The rate of interest is different for each duration.

The 1-year rate is 3.1%. So the 1-year discount factor is 1.031^-1. This should be applied to the cashflow of 10 at time 1.
The 2-year rate is 5.2%. So the 2-year discount factor is 1.052^-2. This should be applied to the cashlfow of 10 at time 2.

Then do the other years similarly.

The rate j is calculated by amending a spot rate, so it is used like a spot rate (ie applying only to specific durations of investment).
 
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