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Math Help - Interest

  1. #1
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    Interest

    Here's the question.

    Sarah Ling is seventeen (17) years old and has big plans to retire when she is fifty (50) years old. She estimates she will need $3,000 at the end of each month for thirty (30) years to live comfortably in her old age and guesses that the interest rate will remain constant at 5% compounded annually during that time. Sarah has $10,000 in savings today and plans to save $2,000 each year to achieve her goal.

    1. What interest rate must Sarah obtain in order to meet her goal? 2. If Sarah can save $3,000 per year, what interest rate must she obtain at minimum to meet her goal? 3. If Sarah defers her retirement plans for five (5) years, and then starts adding $5,000 to her savings each year, will she meet her goal of retiring at five (50)? Assume the interest rate is 6.5% compounded annually for period of time until she reaches fifty (50) years of age.

    Using my financial calculator....
    #1
    -3,000 pmt
    360 n
    0.4074
    comp pv = 565,988.4258

    PV=PMT[(1-(1+I)^-n)/I]
    PV=3000[(1-1.004074)^-360)/0.004074]
    PV=565,988.4258


    -10,000 pv
    -2,000 pmt
    565,988.4258 fv
    n 33
    comp i = 9.2619 %

    #2
    8.0106 %

    It was not taught to use a formula for this But couldn't you use the above formula and isolate for "I"?

    #3
    no
    -5000 pmt
    -10,000 pv
    28 n
    6.5 i
    comp fv = 429, 979.04

    I used theses 2 formula to find the above answer
    fV=PMT[((1+I)^n)-1/I]
    fv=pv(1+I)^n


    Thank you very much to those that will participate.
    Last edited by petedam; July 12th 2010 at 05:21 PM.
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  2. #2
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    you seem smart can you answer my question plz? i have a final exam tomorrow
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  3. #3
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    Quote Originally Posted by Meera123 View Post
    you seem smart can you answer my question plz? i have a final exam tomorrow
    LOL...I am far from it. Just trying to learn. But what is your question?
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  4. #4
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    Ryan took out a 30 year mortgage for $160,000 at 9.8% interest compounded monthly. After he made 12 years of payments he decided to refinance the remaining loan for 25 years at 7.2% interest compounded monthly. What willl be the balance on their loan 5 years after the refinance?

    I would reeeally appreciate your help. I'm an 18 year old first year student in a university in Dubai and I'm reeeally dumb.
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  5. #5
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    Pete, you have pressed all the RIGHT keys, including the rate conversion to .4074 in part#1:
    youze a QUICK learner. We all stand up here and give you a standing ovation!!

    An important question now is:
    if you had no "financial calculator", could you get those same results using appropriate formulas?
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  6. #6
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    Quote Originally Posted by Wilmer View Post
    Pete, you have pressed all the RIGHT keys, including the rate conversion to .4074 in part#1:
    youze a QUICK learner. We all stand up here and give you a standing ovation!!

    An important question now is:
    if you had no "financial calculator", could you get those same results using appropriate formulas?
    Wilmer...thank you ver much for your comment. The reason I use my calculator is that my intructor prefers that i do it this way, dont know why. To prove to you that I have learned alot i will show you the other way...the algebraic equation way later when i have some more time.
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  7. #7
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    Wilmer..I have edited my original post in red to show the calculation using the formula.
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  8. #8
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    Quote Originally Posted by petedam View Post
    PV=PMT[(1-(1+I)^-n)/I]
    PV=3000[(1-1.004074)^-360)/0.004074]
    PV=565,988.4258

    -10,000 pv
    -2,000 pmt
    565,988.4258 fv
    n 33
    comp i = 9.2619 %

    #2
    8.0106 %

    It was not taught to use a formula for this But couldn't you use the above formula and isolate for "I"?
    No, the "I" cannot be isolated: trial and error is required (known as "iteration".
    I wouldn't worry about it for now if I were you.
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  9. #9
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    Quote Originally Posted by Wilmer View Post
    No, the "I" cannot be isolated: trial and error is required (known as "iteration".
    I wouldn't worry about it for now if I were you.
    I think that will be comming up soon. I have never heard of "iteration" yet. Looking forward to it though.

    Thanks,
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