Final answer:
The accumulated balance after 10 years for an initial investment of $6000 at a 6% APR with interest compounded annually is about $10745.08, calculated using the compound interest formula A = P (1 + r/n)^(nt).
Step-by-step explanation:
To calculate the accumulated balance after 10 years for $6000 invested at an Annual Percentage Rate (APR) of 6% with interest compounded annually, we use the compound interest formula:
A = P (1 + rac{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.
Given:
- P = $6000
- r = 6% or 0.06
- n = 1 (since the interest is compounded annually)
- t = 10 years
Now we can substitute the values into the formula:
A = $6000 (1 + rac{0.06}{1})^{1 × 10}
A = $6000 (1.06)^{10}
Calculate the value inside the parentheses first:
(1.06)^{10} ≈ 1.790847
Then multiply this by the principal amount:
A ≈ $6000 × 1.790847
A ≈ $10745.08
Therefore, the accumulated balance after 10 years is approximately $10745.08.