
What is the compound interest if $45,000 is invested for 15 years at 8% compounded continuously? (Round your answer to the nearest cent.)


To calculate the compound interest for an investment compounded continuously, we use the formula:

\[
A = Pe^{rt}
\]

where:
- $ A $ is the amount of money accumulated after time $ t $,
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (in decimal),
- $ t $ is the time in years,
- $ e $ is the base of the natural logarithm (approximately equal to 2.71828).

Given:
- $ P = 45,000 $
- $ r = 0.08 $ (8% as a decimal)
- $ t = 15 $

Substituting the values into the formula:

\[
A = 45000 \times e^{0.08 \times 15}
\]

Calculating $ e^{0.08 \times 15} $:

\[
0.08 \times 15 = 1.2
\]
\[
A = 45000 \times e^{1.2} \approx 45000 \times 3.3201 \approx 149,404.50
\]

The compound interest is calculated as:

\[
\text{Compound Interest} = A - P = 149,404.50 - 45,000 = 104,404.50
\]

Thus, the compound interest is approximately **$104,404.50**.

Would you like more details on the calculation, or do you have any questions? Here are some related questions you might consider:

1. How does continuous compounding compare to annual compounding?
2. What would the compound interest be if the rate were 6% instead?
3. How does changing the investment period to 10 years affect the interest?
4. What is the formula for calculating compound interest for non-continuous compounding?
5. How would you calculate the total amount if you were to invest monthly instead of as a lump sum?

**Tip:** For continuous compounding, the rate of interest plays a significant role; even small changes in the rate can lead to significant differences in the final amount.

What is the compound interest if $45,000 is invested for 15 years at 8% compounded continuously? (Round your answer to the nearest cent.)

Discover how to calculate the compound interest on an investment of $45,000 at an 8% annual interest rate compounded continuously over 15 years. The final amount is approximately $149,404.50, leading to a compound interest of $104,404.50.

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