math(simple interest)

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Suppose that the current rates on 60- and 120-day GICs(Guaranteed Investment Certificates) are 5.50% and 5.75%, respectively. An investor is weighing the alternatives of purchasing a 120-day GIC versus purchasing a 60-day GIC and then reinvesting its maturity value in a second 60-day GIC. What would the interest rate on 60-day GICs have to b 60 days from now for the investor to end up in the same financial position with either alternative?

  • math(simple interest) -

    Since they are short term instruments, they pay simple interest.
    $1000 invested in a 120 day GIC collects insterest of the amount
    I1=1000*0.0575*120/365=$18.90411
    $1000 invested in a 60 day GIC collects interest
    I2=1000*0.0550*60/365=$9.041096
    Therefore the amount needed for the next 60 days
    = $18.90411 - $9.041096
    = $9.86301
    Effective interest rate
    = 9.86301/60*365/1000
    = 0.06
    It will require 6% interest for the GIC for the next 60 days to catch up with the equivalent of the 120-day GIC.

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