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    8. Amy plans to join a savings scheme in which she will pay in £500 at the start of each year.
    One scheme that she is considering pays 6% interest on the amount in the account at the end of each year.
    For this scheme,
    (a) find the amount of interest paid into the account at the end of the second year, (3)
    (b) show that after interest is paid at the end of the eighth year, the amount in the account will be £5246 to the nearest pound. (4)
    Another scheme that she is considering pays 0.5% interest on the amount in the account at the end of each month.
    (c) Find, to the nearest pound, how much more or less will be in the account at the end of the eighth year under this scheme. (5)

    (1.005)^12 = 1.0617...
    end of 8th year: 500 × 1.0617[(1.0617)^8 −1]/(1.0617-1) = 5285.71

    £40 more in account

    In here,I dont understand why (1.005)^12 = 1.0617...???
    Could anyone please explain?


    If you multiply something by 1 then it is 100% of that original value. Multiplying by 1.1 is 110% of the original value, so 1.005 is the original value plus 0.5% (or 100.5% of the original value). You do this by the power of 12 because the increase is done 12 times per year (at the end of each month).

    ^12 means to the power of 12. You can't just add 12 * 0.5% of the original value, because it is done per month and so the amount that is being multiplied by 100.5% is changing each month. Hope this makes sense.
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Updated: January 3, 2013

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