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Charlotte opened a savings account and deposited $800.00\$800.00 as principal. The account earns 8%8\% interest, compounded annually. What is the balance after 1010 years?\newlineUse the formula A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}, where AA is the balance (final amount), PP is the principal (starting amount), rr is the interest rate expressed as a decimal, nn is the number of times per year that the interest is compounded, and tt is the time in years.\newlineRound your answer to the nearest cent.

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Q. Charlotte opened a savings account and deposited $800.00\$800.00 as principal. The account earns 8%8\% interest, compounded annually. What is the balance after 1010 years?\newlineUse the formula A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}, where AA is the balance (final amount), PP is the principal (starting amount), rr is the interest rate expressed as a decimal, nn is the number of times per year that the interest is compounded, and tt is the time in years.\newlineRound your answer to the nearest cent.
  1. Identify values: Identify the values of PP, rr, nn, and tt.
    Principal amount (PP) = $800.00\$800.00
    Interest rate (rr) = 8%8\% annually
    Number of times interest is compounded per year (nn) = 11 (since it's compounded annually)
    Time in years (tt) = 1010 years
  2. Convert interest rate: Convert the annual interest rate from a percentage to a decimal.\newline r=8%=8100=0.08r = 8\% = \frac{8}{100} = 0.08
  3. Substitute into formula: Substitute the values into the compound interest formula A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}\newlineA=800(1+0.081)(1×10)A = 800(1 + \frac{0.08}{1})^{(1 \times 10)}
  4. Simplify expression: Simplify the expression inside the parentheses.\newline1+0.081=1+0.08=1.081 + \frac{0.08}{1} = 1 + 0.08 = 1.08
  5. Calculate final amount: Calculate the final amount AA using the simplified expression.A=800×(1.08)10A = 800 \times (1.08)^{10}
  6. Perform exponentiation: Perform the exponentiation.\newline(1.08)102.158925(1.08)^{10} \approx 2.158925
  7. Multiply principal amount: Multiply the principal amount by the result of the exponentiation to find the final balance.\newlineA=800×2.1589251727.14A = 800 \times 2.158925 \approx 1727.14

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