Final answer:
The ending balance of $1,500 deposited at an annual interest rate of 2.5%, compounded continuously, after 3 years is approximately $1,616.95.
Step-by-step explanation:
To calculate the ending balance of a deposit of $1,500 at an annual interest rate of 2.5%, compounded continuously, over 3 years, we will use the formula for continuous compounding, which is: A = Pert
{ Where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial sum of money), r is the annual interest rate (decimal), t is the time the money is invested for in years, and e is the base of the natural logarithm, approximated as 2.71828 }.
Let's do the calculation step by step:
- Principal amount (P) = $1,500
- Annual interest rate (r) = 2.5% or 0.025 (as a decimal)
- Time (t) = 3 years
Substitute these values into the formula:
A = 1500 * e(0.025*3)
Now calculate the exponent:
e(0.025*3) ≈ e0.075
≈ 1.07797 (rounded to five decimal places)
Finally, calculate the ending balance:
A = 1500 * 1.07797
≈ $1,616.95
Therefore, the ending balance after 3 years, to the nearest cent, would be $1,616.95.