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20 August, 07:36

Jane has two savings accounts, Account S and Account C. Both accounts are opened with an initial deposit of $300 and an annual interest rate of 3.5%. No additional deposits are made, and no withdrawals are made. Account S earns simple interest, and Account C earns interest compounded annually. Which account will earn more interest after 10 years? How much more?

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  1. 20 August, 08:32
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    Step-by-step explanation:

    The formula for determining simple interest is expressed as

    I = PRT/100

    Where

    I represents interest paid on the investment.

    P represents the principal or amount invested.

    R represents interest rate

    T represents the duration of the investment.

    Considering account S,

    P = $300

    R = 3.5%

    T = 10 years

    I = (300 * 3.5 * 10) / 100 = $105

    Considering account C, we would apply the formula for determining compound interest which is expressed as

    A = P (1 + r/n) ^nt

    Where

    A = total amount in the account at the end of t years

    r represents the interest rate.

    n represents the periodic interval at which it was compounded.

    P represents the principal or initial amount deposited

    From the information given,

    P = 300

    r = 3.5% = 3.5/100 = 0.035

    n = 1 because it was compounded once in a year.

    t = 10 years

    Therefore,

    A = 300 (1 + 0.035/1) ^1 * 10

    A = 300 (1.035) ^10

    A = $423

    Interest = 423 - 300 = $123

    Account C will earn more. The amount by which it will earn more that account S is

    123 - 105 = $18
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