Final answer:
To calculate the amount of money in the account after 5 years with continuous compounding, we can use the formula A = P * e^(rt). Plugging in the values from the question, we find that there would be approximately $2,927.42 in the account after 5 years.
Step-by-step explanation:
To calculate the amount of money in the account after 5 years with continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
- A is the final amount in the account
- P is the initial investment
- e is the base of the natural logarithm (approximately 2.71828)
- r is the interest rate (in decimal form)
- t is the time period (in years)
Plugging in the values for this problem, we have:
A = $2,700 * e^(0.016 * 5)
A = $2,700 * e^0.08
Using a calculator, we find that e^0.08 is approximately 1.08328706767. Multiplying this by $2,700 gives us:
A = $2,700 * 1.08328706767 = $2,927.42
Therefore, to the nearest cent, there would be approximately $2,927.42 in the account after 5 years.