If you deposit $1000 in a savings account with an interest rate of r compounded annually?

If you deposit $1000 in a savings account with an interest rate of r compounded annually, then the balance in the account after 3 years is given by the function B(c)=1000(1+r)^3, where r is written as a decimal.

What is the formula for the interest rate, r; required to achieve a balance of B in the account after 3 years?

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  • 1 year ago
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    You are given the equation:

    B = 1000(1 + r)³

    And asked to solve for r in terms of B. So let's start with dividing 1000 from both sides:

    B / 1000 = (1 + r)³

    Now we can get the cube root of both sides:

    ∛(B / 1000) = 1 + r

    And finally, subtract 1 from both sides:

    r = ∛(B / 1000) - 1

    Since 1000 = 10³, we can simplify that to be:

    r = ∛(B / 10³) - 1

    r = ∛(B) / 10 - 1

    This matches option B of your choices.

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