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Payment stream question

H

hatton02

Member
This is a general question but is easier explained using a question from the Q+A bank, question 1.39.

Without typing the whole question, I get the point in the answers where they find the present value at time 7. That's OK. My question comes from when they want to move it back to time 6 and then time 5. I understand the need to split it as the values given for the force of interest change at time 6. However, why in the answers do they use integrals as discount factors?

When I first attempted this I thought, at t=6, the force of interest is 0.01+0.003x6 = 0.028. Since i = e^delta - 1, I worked out v. This was then my discount factor from 7 to 6 but this doesn't agree with the integral. Is it because it's a continuous payment that they use integrals and my calculation would be right if the force of interest was only applied once in the year? I'm a bit confused (although can do similar questions in future by remembering to use integrals).

TIA
 
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hatton02 said:
This is a general question but is easier explained using a question from the Q+A bank, question 1.39.

Without typing the whole question, I get the point in the answers where they find the present value at time 7. That's OK. My question comes from when they want to move it back to time 6 and then time 5. I understand the need to split it as the values given for the force of interest change at time 6. However, why in the answers do they use integrals as discount factors?

When I first attempted this I thought, at t=6, the force of interest is 0.01+0.003x6 = 0.028. Since i = e^delta - 1, I worked out v. This was then my discount factor from 7 to 6 but this doesn't agree with the integral. Is it because it's a continuous payment that they use integrals and my calculation would be right if the force of interest was only applied once in the year? I'm a bit confused (although can do similar questions in future by remembering to use integrals).

TIA
Click to expand...

It's not because of the payment stream (as we have effectively replaced it with a single payment of value 6.5740 at time 7). It's because the interest changes continuously. hence calculating the interest for the instant at t=6 cannot then be applied to whole time period between 6 and 7.

Does that help?
 
John Lee said:
It's not because of the payment stream (as we have effectively replaced it with a single payment of value 6.5740 at time 7). It's because the interest changes continuously. hence calculating the interest for the instant at t=6 cannot then be applied to whole time period between 6 and 7.

Does that help?
Click to expand...

Yes, thankyou. I thought it must be to do with being continuous, just was a little unsure as I learnt that the force of interest was a continous function anyway so didn't think it needed an integral in the answer.
 
Hii
Anyone please attach some Q&A questions for me .they'll be of great help...
Thanks in advance
 
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