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Thread: Questions From ACTEX Problem

  1. #1
    Actuary.com - Level II Poster
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    Questions From ACTEX Problem

    Hi, I'm going through the Actex manual and I am having problems with two things:

    1) An exercise states "At a nominal interest rate of i convertible semi-annually, an investment of 1000 immediately and 1500 at the end of the fist year will accumulate to 2600 at the end of the second year. Calculate i." Is this misprinted or am i missing something? "an investment of 1000 immediately and 1500 at the end...." is what I'm asking about...

    and

    2) The actex book says, "There is an important distinction here. Under continuous interest at 6% at time 2, a(2)=1.06^2, which is the same amount you would have under annual interest. However, there is a difference at fractional times like t=1.5. For continuous interest, you would have 1.06^1.5 at t=1.5, but for annual interest you still only have 1.06 at t=1.5, because interest is not compounded until t=2. But I try to work exercise 1 which states:

    "Bruce deposits 100 into a bank account. His account is credited interest at a nominal rate of interest of 4% convertible semiannually.

    At the same time, Peter deposits 100 into a separate account. Peter's account is credited interest at a force of interest of d

    After 7.25 years, the alue of each account is the same. Calculate d."

    So for Bruces account doesnt my first paragraph imply that yr=7 is as far as interest is accumulated? The solution manual uses j=(1.02)^.5-1 as the quarterly rate and then compounds Bruce's interest up through 7.25 periods..

    I've been stuck on these all day, so if anyone could help I'd be real appreciative (Theres only a few weeks left before the exam!)

    Thanks,
    Chris K.

  2. #2
    Actuary.com - Level III Poster nostalgiajesskang's Avatar
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    Quote Originally Posted by cknapp1 View Post
    Hi, I'm going through the Actex manual and I am having problems with two things:

    1) An exercise states "At a nominal interest rate of i convertible semi-annually, an investment of 1000 immediately and 1500 at the end of the fist year will accumulate to 2600 at the end of the second year. Calculate i." Is this misprinted or am i missing something? "an investment of 1000 immediately and 1500 at the end...." is what I'm asking about...

    and

    2) The actex book says, "There is an important distinction here. Under continuous interest at 6% at time 2, a(2)=1.06^2, which is the same amount you would have under annual interest. However, there is a difference at fractional times like t=1.5. For continuous interest, you would have 1.06^1.5 at t=1.5, but for annual interest you still only have 1.06 at t=1.5, because interest is not compounded until t=2. But I try to work exercise 1 which states:

    "Bruce deposits 100 into a bank account. His account is credited interest at a nominal rate of interest of 4% convertible semiannually.

    At the same time, Peter deposits 100 into a separate account. Peter's account is credited interest at a force of interest of d

    After 7.25 years, the alue of each account is the same. Calculate d."

    So for Bruces account doesnt my first paragraph imply that yr=7 is as far as interest is accumulated? The solution manual uses j=(1.02)^.5-1 as the quarterly rate and then compounds Bruce's interest up through 7.25 periods..

    I've been stuck on these all day, so if anyone could help I'd be real appreciative (Theres only a few weeks left before the exam!)

    Thanks,
    Chris K.
    For question 1, it means an investment of 1000 immediately and 1500 at the end of year 1 will accumulate to 2600 at the end of second year.

    1000(1+i/2)^4 + 1500(1+i/2)^2 = 2600. Solving for i, I get 0.01402

    My solution for question is
    Bruce = (1.02)^(7.25*2)
    Peter = e^(7.25d)
    (1.02)^(7.25*2) = e^(7.25d)
    d = 0.0396

    The statement in the manual makes sense, but all this while, I just solve it using the way I show above and encounter no problem.

    All the best Chris!

  3. #3
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    1) I think this problem is pretty straight-forward and the previous post answered it correctly.

    2) I think you have to assume with these type of problems that interest is credited continuously. ie. when it states "interest is credited at a nominal rate of interest of 4% convertible semiannually" this is just giving you that rate that you should use; this does not mean, unless specifically stated, that interest is only credited to the account four times per a year.
    hope this helps!

  4. #4
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    another actex practice exam question

    One buys a house for 150,000 with a mortgage rate 5.8% convertible monthly. At the time of purchase he owns a 10,000 20-year zero coupon bond that earns 4% annually. The bond matures in 15 years. He would like to use the proceeds from the bond to make a payment larger than the usual fixed rate payment and pay off the balance of the mortgage after the 180th payment. How much should his monthly payments be?

    solution:
    R*(a-angle-180@0.483%) + 10,000(1.04^20)(V^180)=150,000
    (where V_i=0.483%) --->R=1173

    I thought the 10,000 was the par value, but the solution seems taking it as the price of the bond. What happened to those 5 years that the bond was cashed in advance? Somehow I am having trouble to interprete the problem.

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    kauz:

    I can't find this problem in the ACTEX 2009 FM manual. What page is it on?

  6. #6
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    Sorry, I should mention that it is Q20 (pg PE3-4), practice exam 3, from the Actex 2008 edition.

  7. #7
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    That question in the 2008 edition was replaced in the 2009 edition. Here is the replacement problem:

    A man buys a house using a thirty year mortgage loan for 300,000. The loan has an interest rate of 6% convertible monthly. He also owns a fifteen year zero-coupon bond which will make a payment of 100,000 to him on the same day as he makes the last payment of the fifteenth year of the mortgage. He plans to increase his monthly payment over the first fifteen years so that at the end of year fifteen he can use the 100,000 from the bond to retire the loan. What should his new monthly payment for the first fifteen years be?

    Answer: 2187.71

    You are right, the 100,000 should be the redemption value of the bond.

  8. #8
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    TCGarcia,
    I appreciate you taking the time to find the problem. The updated version is more clearer and straight. Hopefully I will not get caught too much on the wording in the real exam.
    Last edited by kauz; August 5th 2009 at 07:18 PM.

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