To solve this problem, we can use the formula for continuous compounding:

$A = P e^{rt}$

Where:

• $A$ is the future value of the investment ($137,000 in this case),
• $P$ is the initial principal (the amount Jeriel needs to invest),
• $r$ is the annual interest rate (6.5% or 0.065),
• $t$ is the time in years (5 years),
• $e$ is Euler's number (approximately 2.71828).

We are asked to find $P$, so we can rearrange the formula to solve for $P$:

$P = \frac{A}{e^{rt}}$

Substituting the known values:

$P = \frac{137,000}{e^{0.065 \times 5}}$

Now, let's compute this value.

$P = \frac{137,000}{e^{0.325}} \approx \frac{137,000}{1.384} \approx 99,090.38$

So, Jeriel would need to invest $99,090.38 for the account to reach $137,000 in 5 years with a continuous compounding interest rate of 6.5%.

Would you like to go over the details of the calculation, or is there anything else you'd like to clarify?

Related Questions:

1. How does the continuous compounding formula differ from other types of compounding, like annual or monthly compounding?
2. If the interest rate were increased to 8%, how would that affect the initial investment required to reach $137,000?
3. How would the time period (5 years) impact the required initial investment if the interest rate remained the same?
4. What is the effect of changing the compounding frequency on the amount of interest earned?
5. How could Jeriel track the growth of his investment over time using the continuous compounding formula?

Tip:

When dealing with continuous compounding, remember that the formula involves Euler's number, $e$, which is a constant and plays a crucial role in exponential growth calculations.