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# Thread: FM question

1. ## FM question

Here is the question (Course 2 Exam - May/2000/ Q #37).... A customer is offered an investment where interest is calculated according to the following force of interest: .02t Between time 0 and 3 (inclusive) and .045 at time greater than 3.
The customer invests 1000 at time t=0. What nominal rate of interest, compounded quarterly, is earned over the first four-year period?

I believe i understand how to do it. I am just having a minor complication. I hope this makes sense.....
I want to discuss finding the a(4), using the force of interest given in the question. So what should be done is a(3) multiplied by the accumulated value of just the 4th year. Here is where I get confused.

The accumulated value of just the 4th year should be the a(4)/a(3). (Even if you use integrals). a(4) uses a different force of interest than a(3). So if i use integrals how does it make sense to say e^integral(3 to 4) of .045 dt? We are finding a(4) and then subtracting the three previous years. But the 3 previous years is measured with a different force of interest?!!

I hope this makes sense. Im sure there is a simple answer to this, but i am just confused. Thanks in advance for all your help.  Reply With Quote

2. I think you are misinterpreting the problem.
What does this investment look like 4 years?
e^ (Int from 0 to 3) * e^ (Int from 3 to 4)

Now what nominal interest rate compounded quarterly would yield the same result?  Reply With Quote

3. Originally Posted by trsspidey I think you are misinterpreting the problem.
What does this investment look like 4 years?
e^ (Int from 0 to 3) * e^ (Int from 3 to 4)

Now what nominal interest rate compounded quarterly would yield the same result?
I understand what your saying. I just want to understand the mechanics behind that work. e^ (Int from 3 to 4) is like saying the amount at time 4 minus the amount at time 3. What i dont understand is that it is using the force of interest of time greater than 3?!
Thanks  Reply With Quote

4. Originally Posted by JS415 I understand what your saying. I just want to understand the mechanics behind that work. e^ (Int from 3 to 4) is like saying the amount at time 4 minus the amount at time 3. What i dont understand is that it is using the force of interest of time greater than 3?!
Thanks
What you described there as the amount at time 4 minus the amount at time 3 is how much interest you gained on your investment between time 3 and 4.
You don't understand why it uses a different force of interest at time greater than 3? Well because simply enough....the problems says so! :P

Sorry if I'm not understanding your question! Hopefully someone else can clarify.  Reply With Quote

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