Answer:
None of the given options (A, B, C, D) match the correct investment amount.
Explaination:
A = P * e^(rt),
where:
A = the future amount (in this case, $34,000),
P = the principal amount (the initial investment),
e = Euler's number (approximately 2.71828),
r = the interest rate (2.9% expressed as a decimal, so 0.029),
t = the time period (18 years).
We can rearrange the formula to solve for P:
P = A / e^(rt).
Now we can plug in the given values and calculate the investment amount:
P = $34,000 / e^(0.029 * 18).
Using a calculator, we can evaluate e^(0.029 * 18) and divide $34,000 by the result to find the investment amount.
Calculating e^(0.029 * 18) gives us approximately 1.604.
P = $34,000 / 1.604 ≈ $21,179.55