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Math Help - find the rate, solve for r

  1. #1
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    find the rate, solve for r

    I ussually dont need help for the types of question, but I am having alot of diffuculty isolating r by itself on one side of the = sign.

    Assume a person invests $210 at the end of each year for 10 years at an annual interest rate of r. The ammount of money, A, in the account after 10 years is
    A = \frac{210((1+r)^{10}-1)}{r}

    his goal is to have 3089 in his account after 10 years.

    \frac{210((1+r)^{10}-1)}{r}= 3089
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  2. #2
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    Re: find the rate, solve for r

    Quote Originally Posted by delgeezee View Post
    I ussually dont need help for the types of question, but I am having alot of diffuculty isolating r by itself on one side of the = sign.

    Assume a person invests $210 at the end of each year for 10 years at an annual interest rate of r. The ammount of money, A, in the account after 10 years is
    A = \frac{210((1+r)^{10}-1)}{r}

    his goal is to have 3089 in his account after 10 years.

    \frac{210((1+r)^{10}-1)}{r}= 3089
    This is an equation of 9th degree in r. I doubt that you'll find a solution in closed form.

    Re-arrange the equation to

    (1+r)^{10}-\frac{3089}{210} r -1 =0

    and use (for instance) Newton's method to get an approximate value of r.

    I've got r \approx 0.08321
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