Final answer:
The compound amount after depositing $2,000 at 6.45% interest compounded continuously for 4 years is $2,588.98. The interest earned is $588.98, which is calculated by subtracting the original principal from the compound amount.
Step-by-step explanation:
The student is asking for the compound amount and the amount of interest earned from a deposit of $2,000 at an annual interest rate of 6.45% that is compounded continuously for 4 years. To solve this, we can use the formula for continuous compounding, which is A = Pert, where P is the principal amount, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.71828.
In this case, P = $2,000, r = 0.0645, and t = 4 years.
Plugging these values into the formula, we get:
A = $2,000 * e(0.0645 * 4)
We calculate the exponential part using a calculator and find that:
A ≈ $2,000 * e0.258 = $2,000 * 1.29449
Therefore, the compound amount is approximately:
A = $2,000 * 1.29449 = $2,588.98
Finally, to find the interest earned, we subtract the original principal from the compound amount:
Interest Earned = $2,588.98 - $2,000 = $588.98
Thus, the compound amount is $2,588.98, and the interest earned is $588.98.