Carson invested $2,700 in an account paying an interest rate of 1.6% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 5 years?

To solve this problem, we will use the formula for continuous compounding interest, which is:

$A = P e^{rt}$

where:

• $A$ is the amount of money accumulated after n years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $t$ is the time the money is invested for, in years.
• $e$ is the base of the natural logarithm, approximately equal to 2.71828.

Given:

• $P = 2700$ dollars
• $r = 1.6\% = 0.016$
• $t = 5$ years

We substitute these values into the formula:

$A = 2700 \times e^{(0.016 \times 5)}$

First, calculate the exponent:

$0.016 \times 5 = 0.08$

Next, calculate $e^{0.08}$:

$e^{0.08} \approx 1.08328706767$

Now, multiply this by the principal amount:

$A = 2700 \times 1.08328706767 \approx 2924.875683$

Rounding to the nearest cent:

$A \approx 2924.88$

Therefore, the amount of money in the account after 5 years would be approximately $2,924.88.