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Jayce and Savannah deposit $10,000.00\$10,000.00 into a savings account which earns 4%4\% interest compounded annually. They want to use the money in the account to go on a trip in 22 years. How much will they be able to spend? Use 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. Round your answer to the nearest cent.

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Q. Jayce and Savannah deposit $10,000.00\$10,000.00 into a savings account which earns 4%4\% interest compounded annually. They want to use the money in the account to go on a trip in 22 years. How much will they be able to spend? Use 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. Round your answer to the nearest cent.
  1. Identify Values: First, let's identify the values we need to plug into the formula A=P(1+rn)ntA=P(1+ \frac{r}{n})^{nt}.P=$10,000.00P = \$10,000.00, r=4%r = 4\% or 0.040.04 as a decimal, n=1n = 1 (since it's compounded annually), and t=2t = 2 years.
  2. Plug into Formula: Now, let's plug these values into the formula. A=10000(1+0.041)(12)A = 10000(1 + \frac{0.04}{1})^{(1\cdot2)}
  3. Simplify Equation: Simplify the equation inside the parentheses.\newlineA=10000(1+0.04)2A = 10000(1 + 0.04)^{2}
  4. Add Numbers: Add the numbers inside the parentheses.\newlineA=10000(1.04)2A = 10000(1.04)^{2}
  5. Calculate Power: Calculate the power of 1.041.04 squared.\newlineA=10000×1.0816A = 10000 \times 1.0816
  6. Multiply Amounts: Multiply the principal amount by the result.\newlineA=10000×1.0816=10816A = 10000 \times 1.0816 = 10816
  7. Round Answer: Round the answer to the nearest cent.\newlineA=$10,816.00A = \$10,816.00

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