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Math Help - sum

  1. #1
    Junior Member VDestinV's Avatar
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    sum

    51. Jose wants to find a savings plan that will accumulate to $1 000 000 by the time he retires. He plans to retire in 35 years. He is willing to make monthly payments of $200. What interest rate will allow Jose to do this?

    52. Investigate different savings plans that will accumulate to $100 000 after 15 years.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by VDestinV View Post
    51. Jose wants to find a savings plan that will accumulate to $1 000 000 by the time he retires. He plans to retire in 35 years. He is willing to make monthly payments of $200. What interest rate will allow Jose to do this?
    What have you tried? Your interest rate is not defined very well. This leaves the problem statement open to various interpretations. Shall we assume monthly compounding?

    Let's say the MONTHLY effective rate is 'i' and r = 1+i

    Then: 200*(r + r^{2} + r^{3} + ... + r^{35*12}) = 1000000

    Solve for 'i' and then maybe convert to ANNUAL EFFECTIVE or ANNUAL NOMINAL or whatever it is you think the question wants.

    Hint: r + r^{2} + r^{3} + ... + r^{35*12} = \frac{r-r^{421}}{1-r} if that helps.

    Show you work. So far, I've seen nothing.
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