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22 November, 20:53

Korey and Lauren decided they needed to see their local bank to check on their accounts.

Korey thinks that they should deposit $500 for the initial amount. This account has a 3% interest rate that is compounded quarterly.

Lauren thinks that they should deposit $500 for the initial amount. This account has a 4% interest rate that is compounded monthly.

Who's idea will really pay off? Which method would be the best for having more money after leaving the money untouched for 2 years.

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  1. 22 November, 21:02
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    Lauren's method would be the best for having more money after leaving the initial deposit untouched for 2 years.

    Step-by-step explanation:

    1. Let's review the information given to us to answer the question correctly:

    Initial amount = $ 500

    Korey's interest rate = 3% compounded quarterly = 0.03/4

    Lauren's interest rate = 4% compounded monthly = 0.04/12

    2. Who's idea will really pay off? Which method would be the best for having more money after leaving the money untouched for 2 years.

    Let's use the compound interest formula this way:

    A = P * (1 + r/n) ⁿˣ, where:

    A = final balance of the account

    P = initial deposit ($ 250)

    r = interest rate (0.03/4 or 0.04/12)

    n = number of times interest applied per time period (4 quarters or 12 months)

    x = number of time periods elapsed (2 years)

    Now we can calculate Korey's method this way:

    A = 500 * (1 + 0.03/4) ⁴°²

    A = 500 * (1.0075) ⁸

    A = 500 * 1.061598848

    A = $ 530.80 (Rounding to the next cent)

    Now we can calculate Lauren's method this way:

    A = 500 * (1 + 0.04/12) ¹²°²

    A = 500 * (1.0033) ²⁴

    A = 500 * 1.083142959

    A = $ 541.57 (Rounding to the next cent)

    Lauren's method would be the best for having more money after leaving the initial deposit untouched for 2 years.
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