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Math Help - Calculating Equivalent GIC (simple interest)

  1. #1
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    Calculating Equivalent GIC (simple interest)

    Rob has $1,000 to invest for 120 days and is considering two options.



    Option 1: He can invest the money in a 120-day GIC paying simple interest of 4.48%.



    Option 2: He can invest the money in a 60-day GIC paying simple interest of 4.50% and then re-invest the maturity value into another 60-day GIC.



    What would the interest rate on the second 60-day GIC have to be for both options to be equivalent?


    So far I have got:


    Option 1:
    1000(1+.0448)(120/365)=1014.73


    Option 2:
    1000(1+.045)(60/365)=1007.39


    1007.39(1+.45)(60/365)=1014.84


    I know i should use the formula R=I/PT im just not sure what numbers to plug in to find the equivalent rate.. Can anyone show me how to solve this? The answer is not in the back of the book.
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  2. #2
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    Quote Originally Posted by Adam123 View Post
    Rob has $1,000 to invest for 120 days and is considering two options.



    Option 1: He can invest the money in a 120-day GIC paying simple interest of 4.48%.



    Option 2: He can invest the money in a 60-day GIC paying simple interest of 4.50% and then re-invest the maturity value into another 60-day GIC.



    What would the interest rate on the second 60-day GIC have to be for both options to be equivalent?


    So far I have got:


    Option 1:
    1000(1+.0448)(120/365)=1014.73


    Option 2:
    1000(1+.045)(60/365)=1007.39


    1007.39(1+.45)(60/365)=1014.84


    I know i should use the formula R=I/PT im just not sure what numbers to plug in to find the equivalent rate.. Can anyone show me how to solve this? The answer is not in the back of the book.
    What is GIC? If you are going to use acronyms, at least tell us what they mean.
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    What is GIC? If you are going to use acronyms, at least tell us what they mean.
    Guaranteed Investment Certificates

    sorry
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  4. #4
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    Quote Originally Posted by Adam123 View Post
    Guaranteed Investment Certificates

    sorry
    Your formulas are written wrong which was causing me to get odd answers.

    \displaystyle P\left(1+[i\cdot n]\right)\neq P(1+i)n

    \dispalystyle 1000\cdot (1+.0448)\cdot\frac{120}{365}=343.50

    \displaystyle 1000\cdot\left(1+\left[.0448\cdot\frac{120}{365}\right]\right)=1014.73

    \displaystyle 1007.39\cdot\left(1+\left[i\cdot\frac{60}{365}\right]\right)=1014.73
    Last edited by dwsmith; February 1st 2011 at 12:07 PM.
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  5. #5
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    Quote Originally Posted by Adam123 View Post
    So far I have got:
    Option 1:
    1000(1+.0448)(120/365)=1014.73
    Option 2:
    1000(1+.045)(60/365)=1007.39
    1007.39(1+.45)(60/365)=1014.84
    Change last line: 1007.39(1 + r)(60/365) = 1014.73
    Solve for r
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  6. #6
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    R(interest rate) is what im trying to figure out im not sure what numbers to put in to find the interest rate.
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  7. #7
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    Quote Originally Posted by Adam123 View Post
    R(interest rate) is what im trying to figure out im not sure what numbers to put in to find the interest rate.
    I edited my post. Your formulas weren't correct.
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  8. #8
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    How do I solve for I? to get the interest rate
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  9. #9
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    Quote Originally Posted by Adam123 View Post
    How do I solve for I? to get the interest rate
    \displaystyle \frac{1}{1007.39}\left[1007.39\cdot\left(1+\left[i\cdot\frac{60}{365}\right]\right)\left]=1014.73\cdot\frac{1}{1007.39}

    \displaystyle 1+\left[i\cdot\frac{60}{365}\right]-1=\frac{1014.73}{1007.39}-1

    \displaystyle \left[i\cdot\frac{60}{365}\right]=\frac{1014.73}{1007.39}-1\Rightarrow\cdots
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  10. #10
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    I'm not sure how to use that to calculate what the interest rate should be for the second one
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  11. #11
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    Quote Originally Posted by Adam123 View Post
    I'm not sure how to use that to calculate what the interest rate should be for the second one
    i is the interest rate for the second one.

    \displaystyle 1007.39\cdot\left(1+\left[i\cdot\frac{60}{365}\right]\right)=1014.73

    Solve for i and you have the answer.
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  12. #12
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    How do I solve for i?

    the formula I learned was R(rate)=I/Pt

    so R(rate)=7.34/1007.39(60/365)
    R= .0443 4.43%?

    awesome it worked.. thankyou so much!!

    i went and plugged that into your formula

    1007.39 (1+ [.0443(60/365]) =1014.726 rounded to 1014.73
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  13. #13
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    Quote Originally Posted by Adam123 View Post
    How do I solve for i?
    Post 9
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  14. #14
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    Cool Re: Calculating Equivalent GIC (simple interest)

    I was stuck on a similiar question, i think i got it after countless hours! lol so heres my solution.
    Your first calculation of 4.5% on a 60 day = $1007.39 (MINUS THAT) from the Found MATURITY VALUE of THE 120 day of $1014.73
    which will give you a difference of $7.34.

    Which means for your 2nd 60 day calculation you want the RATE (in percentage) difference from $1007.39 to $1014.73
    So the then you plug into the formula you had ... R=I/PT

    OVERALL interest in dollar amount : was ... R = $7.34 (interest) DIVIDED BY : $1007.39(1st principal amount first 60 day) x 60 (2nd 60day) / divided by 365 days

    will give you R = $7.34 / 165.60
    which equals RATE OF CHANGE = 0.044324111 X 100 %

    EQUALS = 4.432 % WOULD BE THE INTEREST RATE ON THE 2ND 60 DAY GIC TO BE EQUIVALENT...

    Hope that is correct and therefore hope it may help... feel free to correct and feedback... :O) I tried...
    Last edited by abegail; November 25th 2012 at 03:56 PM. Reason: typing error
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