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Get Rich Quick Investments LTD offers 2 investment schemes.
Scheme 1: Earn 6.5% interest per year, compounded monthly.
Scheme 2: Earn 6.45% interest per year, compounded daily.
An investor reasons that Scheme 2 should be the best because its interest rate is very close to 6.5%, but the compounding occurs daily. Using each scheme, compare how long it would take to double your investment, and hence determine whether the investor is correct.

  • Maths -

    A simple way to see which is the higher rate is to take an arbitrary amount of money, say $100, and see how much it grows to in one year
    Scheme 1: amount = 100(1 + .065/12)^12 = 106.697
    Scheme 2: amount = 100(1 + .0645/365)^365 = 106.662

    so what do you think?

    Let's find the effective annual rate of each
    we can get it by dividing our answers above by 100
    scheme 1: annual rate = 6.697%
    scheme 2 : annual rate = 6.662%

    so solving for
    2 = 1(1.06697)^n
    n = log 2/log 1.06697 = 10.69 years

    for scheme 2:
    2 = 1(1.06662)^n
    n = log2/log 1.06662) = 10.75 years

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