Final answer:
To find the balance after 540 years, the compound interest formula A = P(1 + r/n)^(nt) is used, plugging in the principal amount of $215, the annual interest rate of 2% as a decimal (0.02), and the time of 540 years.
Step-by-step explanation:
To calculate the balance obtained by investing $215 at a rate of 2% with annual compounding after 540 years, we use the formula for compound interest:
A = P(1 + r/n)nt
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
For this question:
- P = $215
- r = 0.02 (2% expressed as a decimal)
- n = 1 (since the interest is compounded annually)
- t = 540 years
Plugging these values into the formula:
A = 215(1 + 0.02)540
Now, we calculate the amount A using a calculator.