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Interest on principal over 5 years

  1. Aug 12, 2005 #1
    A retired hockey star wants to set up a scholarship fund to assist an underprivileged child who would like to go to a post-secondary institution. He wants to ensure that the student will have $6000 per year for five years. How much should he give to the institution, now, to ensure that this can happen, if the institution is able to invest the money at 10%/a compounded annually?

    a)Set up a line diagram showing the present value of each of the $6000 payments.
    Note: You will need to find the present value of an amount when calculating the present value of each $6000 payment.

    b)Explain why the amounts form a geometric series.

    c)Calculate the sum of this geometric series using . Sn=( a(r^n-1)) / (r-1)



    a) okay so it goes 6000,6000/(1.1)^1 ... 6000/(1.1)^4 (1+i)=1.1

    b) it is geometric because the ratio btwn consecutive terms are constant

    c) Okay now i dont know how to sub in and then solve it because i dont know A because i am assuming that he is giving 1 payment for the whole 5 years the kid is going to an university. and i dont know Sn because i am SOLVING for Sn so how do i sub for r and how do i solve?
     
  2. jcsd
  3. Aug 13, 2005 #2

    Fermat

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    He is unlikely to give a single payment to cover the student's costs for the whole 5 years but rather 5 separate payments, each one at the start of the currrent year of study.

    A Geometric series is,

    S = {a, ar, ar², ..., ar^(n-1)}

    where a is the initial term,
    r is the common ratio

    You already used r when creating your line diagram which, in fact, is just the set S.
     
  4. Aug 13, 2005 #3
    well if he does that then it would just be five $6000 payments and the question doesent say WHEN he is giving this money to start saving
     
  5. Aug 13, 2005 #4

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    According to the question, as you posted it, he gives the money now.

    I imagine that means just before the start of the 1st year's study

    Although 5 separate payments of $6000 are made, the amount the hockey star gives to the institution for investment is Sn.
     
  6. Aug 13, 2005 #5
    yes that is what got from the question as well that means that there are 5 payments of 6000 to the school. the hockey star pay gives only 1 one payment.

    so that means what i did for a) was correct right? my problem is i dont know how to sub that into the equation of Sn
     
  7. Aug 13, 2005 #6

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    What you did for a) is correct.

    The series you got is,

    6000,6000/(1.1)^1 ... 6000/(1.1)^4

    A Geometric series is,

    S = {a, ar, ar², ..., ar^(n-1)}

    If you compare your series with the geometric series you will norice that a = 6000 and r = 1/1.1.

    Now sub into Sn = ar^(n-1)) / (r-1)
     
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