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Math Help - Annuities

  1. #1
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    Annuities

    a) Determine the present value on January 1, 2000, of payments of $200 every 6 months from January 1, 2000, through January 1, 2004, inclusive, and $100 every 6 months from July 1, 2004, through January 1, 2010, inclusive, if i = .06.

    I think it might be something like: 100(a angle 8)(0.03) + 100(a angle 20)(0.03) which equals 100((1 - v^8)/0.03) + 100((1 - v^20)/0.03) , v=1/1.03
    But the answer is $2,389.72 which is way off from what I'm getting. Am I even close?

    b) At the beginning of the year Kelly establishes a fund with a deposit of $1000. At the beginning of each month a health club withdraws a $24 fee. The fund earns a nominal rate of interest of 18% compounded monthly. Determine the amount in the fund at the end of the year.

    The only way I can think to do this is calculating each month separately so I know there's a faster way ... Any suggestions?

    Thank you!!
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  2. #2
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    Quote Originally Posted by bart203 View Post
    a) Determine the present value on January 1, 2000, of payments of $200 every 6 months from January 1, 2000, through January 1, 2004, inclusive, and $100 every 6 months from July 1, 2004, through January 1, 2010, inclusive, if i = .06.

    I think it might be something like: 100(a angle 8)(0.03) + 100(a angle 20)(0.03) which equals 100((1 - v^8)/0.03) + 100((1 - v^20)/0.03) , v=1/1.03
    But the answer is $2,389.72 which is way off from what I'm getting. Am I even close?

    b) At the beginning of the year Kelly establishes a fund with a deposit of $1000. At the beginning of each month a health club withdraws a $24 fee. The fund earns a nominal rate of interest of 18% compounded monthly. Determine the amount in the fund at the end of the year.

    The only way I can think to do this is calculating each month separately so I know there's a faster way ... Any suggestions?

    Thank you!!
    a) The first piece has 9 of those $200 payments. It's an annuity due.
    a) Make up your mind on the number of $100 payments. It looks like 12 to me.
    b) You must learn to use "Basic Principles".

    if r = 1 + 0.18/12 = 1.015

    At the end of the year, we have

    1000r^12 -24(r^12 + r^11 + ... + r^1)

    You should be able to add the 12 values in the parentheses and you will nearly be done.
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  3. #3
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    Quote Originally Posted by bart203 View Post
    b) At the beginning of the year Kelly establishes a fund with a deposit of $1000. At the beginning of each month a health club withdraws a $24 fee. The fund earns a nominal rate of interest of 18% compounded monthly. Determine the amount in the fund at the end of the year.
    Simply pretend this is a $1000 loan at monthly payments of $24,
    rate .18/12 per month; what is loan balance after 12 payments?
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  4. #4
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    Quote Originally Posted by bart203 View Post
    a) Determine the present value on January 1, 2000, of payments of $200 every 6 months from January 1, 2000, through January 1, 2004, inclusive, and $100 every 6 months from July 1, 2004, through January 1, 2010, inclusive, if i = .06.
    Interest rate is WHAT? i = .06 means every 6 months, from .12/2 = .06;
    get that straightened out.

    With these, sometimes easier to "see" using future value:
    1) future value of payments of $200 to Jan.1/04
    2) future value of above to Jan.1/10
    3) future value of payments of $100 for same period as in 2)
    Add 'em up, calculate present value.
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