Martin deposits $200 in a savings account that earns 5% annual interest. Four years later, Cary deposits $200 in an account earning the same

Question

Martin deposits $200 in a savings account that earns 5% annual interest. Four years later, Cary deposits $200 in an account earning the same interest. Let M represent the balance in Martin’s account and let C represent the amount of money in Cary’s account.

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Gerda 4 years 2021-08-24T12:20:28+00:00 1 Answers 47 views 0

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  1. Sigrid
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    2021-08-24T12:21:30+00:00
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    Complete question :

    Martin deposits $200 in a savings account that earns 5% annual interest. four years later, cary deposits $200 in an account earning the same interest. let m represent the balance in martins account and let c represent the amount of money in carys account. choose the pair of expressions that describe the accounts y years after martin opened his account. martin: 200(1.05)y cary: 200(1.05)y+4 martin: 200(1.05)y+4 cary: 200(1.05)y4 martin: 200(0.05)y cary: 200(0.05)y4 martin: 200(1.05)y cary: 200(1.05)y4 choose the equation that relates the balances in the accounts y years after martin opened his account. c = m(1.05)4y m = c(1.05)4y c = 1.22m m = 1.22c

    Answer:

    m = m = 200(1.05)^y+4

    c = m = 200(1.05)^y

    m = 1.22c

    Step-by-step explanation:

    The future value can be represented as :

    Future value, F = P(1 + r)^n

    r = interest rate = 5% = 0.05 , n = number of years ;

    For Martin :

    m = 200(1 + 0.05)^n

    For cyan :

    c = 200(1 + 0.05)^n

    y years after Martin

    Cyan opened 4 years after Martin :

    Representing in terms of y

    Cyan = y ; Martin = y +4

    m = m = 200(1.05)^y+4

    c = m = 200(1.05)^y

    From. Indices :

    (1.05)^y+4 = 1.05^y * 1.05^4

    Hence,

    m = 200 * 1.05^y * 1.05^4

    c = 200 * 1.05)^y

    Hence,

    m = c * 1.05^4

    m = c * 1.2155

    m = c * 1.22

    m = 1.22c

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