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?

Answer 1

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}.