Final answer:
Using the formula for continuous compounding, the accumulated amount after 3 years of a $4500 investment at a 5% annual rate is approximately $5228.25, demonstrating how impactful compound interest can be.
Step-by-step explanation:
To find the accumulated amount after 3 years when $4500 is invested at a 5% annual rate compounded continuously, you would use the formula for continuous compounding:
A = Pert
Where:
- A represents the accumulated amount after time t,
- P is the principal amount ($4500),
- e is the base of the natural logarithm (approximately equal to 2.71828),
- r is the annual interest rate (5% or 0.05), and
- t is the time the money is invested for (3 years).
Using these values, we calculate the accumulated amount as follows:
A = 4500e0.05*3 = 4500e0.15 ≈ 4500 * 1.161834
The accumulated amount after 3 years would be approximately $5228.25.
By starting to save money early and allowing it to grow through the power of compound interest, a significant increase in the growth of investments can be observed over time, as seen in the provided example of starting with $3000 and letting it grow at a 7% real annual rate of return.