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19 December, 20:03

Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account.

A $13,000 deposit in an account with an APR of 4.5 %.

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  1. 19 December, 23:31
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    1 yr: $13,598.36 5 yr: $16280.20 20 yr: $31,974.84 APY: 4.6%

    Step-by-step explanation:

    The formula for continuous compounding for t years at an APR of r is ...

    A = Pe^ (rt)

    Then for 1 year, the amount for P=13,000 and r=.045 is ...

    A = $13,000e^ (.045) = $13,598.36

    For 5 years, the amount is ...

    A = $13,000e^ (.045·5) = $16,280.20

    For 20 years, the amount is ...

    A = $13,000e^ (.045·20) = $31,974.84

    __

    The multiplier for 1 year is ...

    e^.045 ≈ 1.04602786 = 1 + APY

    This represents an APY of 4.603%.
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