Final answer:
The balance for an $800 investment at a 4% annual interest rate compounded annually for 15 years is approximately $1440.72 when rounded to the nearest cent.
Step-by-step explanation:
To determine the balance of an $800 investment at a 4% annual interest rate compounded annually for 15 years, you can use the compound interest formula:
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.
Here, P = $800, r = 0.04 (4%), n = 1 (compounded annually), and t = 15 years.
Substituting these values into the formula, we get:
A = 800(1 + 0.04/1)^(1*15)
A = 800(1 + 0.04)^15
A = 800(1.04)^15
Now we calculate (1.04)^15:
A ≈ 800 * 1.8009
A ≈ $1440.72
After 15 years, the investment would grow to approximately $1440.72, when rounded to the nearest cent.