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Nathaniel invested $2,900 in an account paying an interest rate of 5.4% compounded continuously. Assuming no deposits or withdr...Question
David invested $89,000 in an account paying an interest rate of 3.1% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 15 years?
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Answered by
GPT 3.5
The formula for calculating the amount of money in an account with continuous compounding is given by:
\[A = P \cdot e^{rt}\]
where:
- $A$ is the amount of money in the account after $t$ years
- $P$ is the principal amount (initial investment)
- $r$ is the annual interest rate (expressed as a decimal)
- $t$ is the time in years
- $e$ is Euler's number, approximately 2.71828
Plugging in the given values, we have:
\[A = 89000 \cdot e^{0.031 \cdot 15}\]
Calculating $e^{0.031 \cdot 15}$:
\[e^{0.031 \cdot 15} \approx 1.54532\]
Multiplying the principal by this value:
\[A \approx 89000 \cdot 1.54532\]
Rounding to the nearest ten dollars:
\[A \approx \$137,562\]
Therefore, to the nearest ten dollars, there would be approximately $137,562 in the account after 15 years. Answer: \boxed{137,560}.
\[A = P \cdot e^{rt}\]
where:
- $A$ is the amount of money in the account after $t$ years
- $P$ is the principal amount (initial investment)
- $r$ is the annual interest rate (expressed as a decimal)
- $t$ is the time in years
- $e$ is Euler's number, approximately 2.71828
Plugging in the given values, we have:
\[A = 89000 \cdot e^{0.031 \cdot 15}\]
Calculating $e^{0.031 \cdot 15}$:
\[e^{0.031 \cdot 15} \approx 1.54532\]
Multiplying the principal by this value:
\[A \approx 89000 \cdot 1.54532\]
Rounding to the nearest ten dollars:
\[A \approx \$137,562\]
Therefore, to the nearest ten dollars, there would be approximately $137,562 in the account after 15 years. Answer: \boxed{137,560}.