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Math Help - Theory of Interest

  1. #1
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    Theory of Interest

    Smith buys a 1000 Canada savings bond, with an issue date of November 1, paying interest at 11.25% per year. The bond can be cashed in anytime after January 1 of the following year, and it will pay simple interest during the first year of 1/12 of the annual interest for every completed month since November 1. The government allows purchasers to pay for their bonds as late as November 9, with full interest still paid for November. Smith pays 1000 on November 9 and cashes in the bond on the following January 1. What is his equivalent effective annual rate of interest for his transaction?

    The answer should be .1365. I have been trying many different things, but I cannot seem to get it. Any input on how I can go about solving this problem will be greatly appreciated.
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  2. #2
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    Quote Originally Posted by auitto View Post
    Smith buys a 1000 Canada savings bond, with an issue date of November 1, paying interest at 11.25% per year. The bond can be cashed in anytime after January 1 of the following year, and it will pay simple interest during the first year of 1/12 of the annual interest for every completed month since November 1. The government allows purchasers to pay for their bonds as late as November 9, with full interest still paid for November. Smith pays 1000 on November 9 and cashes in the bond on the following January 1. What is his equivalent effective annual rate of interest for his transaction?

    The answer should be .1365. I have been trying many different things, but I cannot seem to get it. Any input on how I can go about solving this problem will be greatly appreciated.
    Well, Smitty will receive 2 month's interest: 1000(.1125 / 6)
    He invested for 21+31 = 52 days ; could be 53 days: depends on 1st/last day
    r/365 * 52 = .1125 / 6
    r = .1316
    I don't know how "they" arrived at .1365 ; looks like we cheat here in HockeyLand!
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  3. #3
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    I have found out how to get the correct solution!

    First we find his accumulated amount, which is 1018.75, since he collects two month's interest.

    Next, we use the following formula to get the effective interest rate:

    <br />
A=A_0(1+i)^t.<br />

    Plugging in the numbers we obtain:

    <br />
1018.75=1000(1+i)^{53/365}\quad ==>\quad i=.1365.<br />

    Thank you Wilmer for your help.
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