Questions: Given the formula : A=P e^r Find the amount of money accumulated if you invested 25,000 at 4.3% interest for 8 years compounded continuously. 779,673.95 26,098.45 35,264.47 None of the above

Solution Steps

To solve this problem, we need to use the formula for continuous compounding, which is \( A = P e^{rt} \). Here, \( P \) is the principal amount (\$25,000), \( r \) is the annual interest rate (4.3% or 0.043), and \( t \) is the time in years (8 years). We will calculate the accumulated amount \( A \) using these values.

We are given the following values:

• Principal amount \( P = 25000 \)
• Annual interest rate \( r = 0.043 \)
• Time in years \( t = 8 \)

We will use the formula for continuous compounding: \[ A = P e^{rt} \] Substituting the known values into the formula: \[ A = 25000 \cdot e^{0.043 \cdot 8} \]

First, we calculate the exponent: \[ 0.043 \cdot 8 = 0.344 \] Now, we find \( e^{0.344} \): \[ e^{0.344} \approx 1.411 \]

Now we can calculate \( A \): \[ A = 25000 \cdot 1.411 \approx 35264.47 \]

Final Answer