Final answer:
To calculate the future value of a $3,000 investment at a 7% interest rate compounded continuously for 18 years, use the formula A = Pe^(rt). A is approximately $10,557.90 when rounded to the nearest cent.
Step-by-step explanation:
The question involves calculating the future value of an initial investment using the formula for continuous compound interest.
The formula for continuous compounding is A = Pert, where P is the principal amount (initial investment), r is the annual interest rate (expressed as a decimal), t is the time in years, and e is the base of the natural logarithm, approximately 2.71828. In this case, an initial investment of $3,000 at a 7% interest rate compounded continuously over 18 years is calculated as follows:
A = 3000 * e(0.07*18)
First, calculate the exponent:
0.07 * 18 = 1.26
Next, raise e to the power of 1.26:
e1.26 ≈ 3.5193
Now, multiply this by the principal amount:
A = 3000 * 3.5193 ≈ $10,557.90
Therefore, the investment will be worth approximately $10,557.90 after 18 years, when rounded to the nearest cent.