Final answer:
The accumulated amount after 2 years if $6500 is invested at 2% per year compounded continuously is approximately $6762.55.
Step-by-step explanation:
To find the accumulated amount after 2 years if $6500 is invested at 2% per year compounded continuously, we can use the formula:
A = P * e^(rt)
Where:
- A is the accumulated amount
- P is the principal amount ($6500 in this case)
- e is the base of the natural logarithm (approximately 2.71828)
- r is the annual interest rate (2% or 0.02 in decimal form)
- t is the number of years (2 in this case)
Plugging in the values into the formula:
A = 6500 * e^(0.02 * 2)
Simplifying the equation:
A ≈ 6500 * e^(0.04)
A ≈ 6500 * 1.040810774
A ≈ $6762.55
The accumulated amount after 2 years is approximately $6762.55.