Final answer:
Using the formula for continuous compounding, A = Pe^(rt), where P is $570, r is 0.04, and t is 10, the amount after 10 years is approximately $973.38, making option 3 the correct answer.
Step-by-step explanation:
If $570 is invested at an interest rate of 4% per year and is compounded continuously, how much will the investment be worth in 10 years? To answer this, we use the formula for continuous compounding:
A = P * e(rt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial sum of money).
- r is the annual interest rate (in decimal form).
- t is the time the money is invested for (in years).
- e is the base of the natural logarithm, approximately equal to 2.71828.
Given that the initial investment P is $570, the annual interest rate r is 0.04, and the time t is 10 years, we can calculate the future value of the investment as follows:
A = 570 * e(0.04 * 10)
After calculating this, we find that A is approximately $973.38. Therefore, option 3) $973.38 is the correct answer.