To determine the amount of money in the account after 16 years, we will use the formula for continuous compound interest:

$V = P e^{rt}$

Where:

• $V$ is the value of the account after $t$ years,
• $P$ is the principal initially invested,
• $r$ is the annual interest rate (as a decimal),
• $t$ is the time in years,
• $e$ is the base of the natural logarithm, approximately 2.71828.

Given values:

• $P = 72,000$ (initial investment),
• $r = 5.1\% = 0.051$ (annual interest rate),
• $t = 16$ years.

Substituting the values into the formula:

$V = 72,000 \times e^{0.051 \times 16}$

Now, calculate the exponent:

$0.051 \times 16 = 0.816$

Then calculate $e^{0.816}$:

$e^{0.816} \approx 2.261$

Now, calculate the final value:

$V = 72,000 \times 2.261 \approx 162,792$

Final Answer:

The amount of money in the account after 16 years is approximately $162,792.00.

Would you like any further explanation or details? Here are some related questions:

1. What would the amount be if the interest rate were 4.5% instead of 5.1%?
2. How would the amount change if the interest were compounded annually instead of continuously?
3. How does the formula for continuous compounding compare to the formula for compound interest with periodic compounding?
4. If the principal were increased to $100,000, what would the value of the account be after 16 years?
5. How does increasing the time period (t) to 20 years affect the final value?

Tip: The power of continuous compounding becomes even more significant as time increases, so investing for longer periods generally results in greater returns.