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19 June, 17:32

Jackson and Olivia deposited $9,047.00 into a savings account which earns interest compounded monthly. After 8 months, they had $9,779.00 in the account which they used to go on a trip. What was the interest rate on the account?

Round your answer to the nearest tenth of a percent.

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  1. 19 June, 18:56
    0
    11.7%

    Step-by-step explanation:

    The account balance (A) for a principal amount P and monthly interest rate r will be ...

    A = P (1 + r) ^8

    Then we can divide by P and take the 8th root to find r:

    A/P = (1+r) ^8

    (A/P) ^ (1/8) = 1 + r

    (A/P) ^ (1/8) - 1 = r

    Since this is the monthly rate, we need to multiply this value by 12 to find the annual interest rate on the account:

    annual rate = 12 ((A/P) ^ (1/8) - 1) = 12 ((9779/9047) ^ (1/8) - 1) ≈ 0.11728 ≈ 11.7%
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