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Thread: Interest rate question

  1. #1
    Actuary.com - Level II Poster
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    Interest rate question

    Hi, I got a problem about the interest rate. Hope someone can help.

    A deposits 100 into a saving account at time 0, which pays nominal interest i, compounded semiannually.

    B deposits 200 into a saving account at time 0, which pay simple interest at an annual rate of i

    A and B earn the same amount of interest during the last 6 months of the 8th year, find i

    my calculation is like this

    A's interest
    100(1 + i/2)^15 - 100

    B's interest
    100(7.5i)

    so
    100(1 + i/2)^15 - 100 =100(7.5i)

    but i cannot get the right answer. Anyone can advise?

    Thanks a lot.

  2. #2
    Actuary.com - Level II Poster lee_onion's Avatar
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    In your solution you calculate the interest of the whole 7.5 years, but in the problem it means the interest during the last 6 months of the 8th year, yes, only 6 months!
    So I think the solution may be:

    A's interest
    100(a(8)-a(7.5)) = 100((1+i/2)^16-(1+i/2)^15) or 100a(7.5)*i/2 = 100((1+i/2)^15)*i/2

    B's interest
    200(a(8)-a(7.5)) = 200(1+8i-1-7.5i) = 200*0.5i

    So 100((1+i/2)^15)*i/2 = 200*0.5i and i = 9.46%

  3. #3
    Actuary.com - Level II Poster
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    Thanks a lot.

    I have misunderstood the question :>

  4. #4
    Actuary.com - Level II Poster lee_onion's Avatar
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    Quote Originally Posted by thtang View Post
    Thanks a lot.

    I have misunderstood the question :>
    Most of the mistakes are caused by our carelessness, I hope our everyone will never do this in the real exam...

  5. #5
    Actuary.com - Level III Poster
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    Help, please.

    I don't understand how: 100((1+i/2)^15)*i/2=100(1+i/2)^16-100(1+i/2)^15


    :confused-:
    There ain't no easy way out.

    -Tom Petty

  6. #6
    Actuary.com - Level II Poster lee_onion's Avatar
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    Quote Originally Posted by Elk View Post
    I don't understand how: 100((1+i/2)^15)*i/2=100(1+i/2)^16-100(1+i/2)^15


    :confused-:
    100(1+i/2)^16-100(1+i/2)^15
    =100(1+i/2)^15 * (1+i/2)-100(1+i/2)^15
    =100(1+i/2)^15 * ((1+i/2)-1)
    =100(1+i/2)^15 * i/2

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