Questions: What is the compound interest if 155,000 is invested for 3 years at 12% compounded continuously. The interest is - (Round to 2 decimal places.)

Solution Steps

To find the compound interest for an investment compounded continuously, we use the formula for continuous compounding: \( A = P \times e^{(r \times t)} \), where \( A \) is the amount after time \( t \), \( P \) is the principal amount, \( r \) is the annual interest rate, and \( t \) is the time in years. The compound interest is then \( A - P \).

Using the formula for continuous compounding, we have:

\[ A = P \times e^{(r \times t)} \]

Substituting the given values:

\[ A = 155000 \times e^{(0.12 \times 3)} \]

Calculating the exponent:

\[ 0.12 \times 3 = 0.36 \]

Thus, we find:

\[ A = 155000 \times e^{0.36} \approx 222166.0593 \]

The compound interest \( CI \) is given by:

\[ CI = A - P \]

Substituting the values we calculated:

\[ CI = 222166.0593 - 155000 \approx 67166.0593 \]

Rounding the compound interest to two decimal places:

\[ CI \approx 67166.06 \]

Final Answer