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Use the compound interest formula to determine the accumulated balance after the stated period. $6000 invested at an APR of 6% for 10 years. If interest is compounded annually, what is the amount of money after 10 years?

User PtrTon
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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.

User Arien Chen
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