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If $700\$700 is invested at 9%9\% compounded\newline(A) annually,\newline(B) quarterly,\newline(C) monthly,\newlinewhat is the amount after 66 years? How much interest is earned?\newline$1,194.04\$1,194.04 (Round to the nearest cent.)\newlineHow much interest is earned?\newline$494.04\$494.04 (Round to the nearest cent.)\newline(C) If it is compounded monthly, what is the amount?\newline$1,198.79\$1,198.79 (Round to the nearest cent.)\newlineHow much interest is earned?\newline$□\$\square (Round to the nearest cent.)

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Q. If $700\$700 is invested at 9%9\% compounded\newline(A) annually,\newline(B) quarterly,\newline(C) monthly,\newlinewhat is the amount after 66 years? How much interest is earned?\newline$1,194.04\$1,194.04 (Round to the nearest cent.)\newlineHow much interest is earned?\newline$494.04\$494.04 (Round to the nearest cent.)\newline(C) If it is compounded monthly, what is the amount?\newline$1,198.79\$1,198.79 (Round to the nearest cent.)\newlineHow much interest is earned?\newline$□\$\square (Round to the nearest cent.)
  1. Identify Variables: First, we need to identify the variables for the compound interest formula, which is A=P(1+r/n)(nt)A = P(1 + r/n)^{(nt)}, where:\newline- AA is the amount of money accumulated after nn years, including interest.\newline- PP is the principal amount (the initial amount of money).\newline- rr is the annual interest rate (decimal).\newline- nn is the number of times that interest is compounded per year.\newline- tt is the time the money is invested for in years.\newlineFor this problem:\newlineP=$700P = \$700 (the initial investment),\newliner=9%r = 9\% or 0.090.09 (the annual interest rate in decimal form),\newlineAA00 (since the interest is compounded monthly),\newlineAA11 (the time in years the money is invested).
  2. Calculate Amount: Now we will calculate the amount AA after 66 years using the compound interest formula.A=700×(1+0.0912)(12×6)A = 700 \times (1 + \frac{0.09}{12})^{(12\times6)}
  3. Perform Division: Perform the division inside the parentheses.\newlineA=700×(1+0.0075)72A = 700 \times (1 + 0.0075)^{72}
  4. Add Numbers: Add the numbers inside the parentheses.\newlineA=700×(1.0075)72A = 700 \times (1.0075)^{72}
  5. Calculate Exponentiation: Calculate the exponentiation.\newlineA≈700×(1.0075)72A \approx 700 \times (1.0075)^{72}\newlineA≈700×1.7138A \approx 700 \times 1.7138
  6. Multiply Principal Amount: Multiply the principal amount by the result of the exponentiation to find the total amount.\newlineA≈700×1.7138A \approx 700 \times 1.7138\newlineA≈$(1,199.66)A \approx \$(1,199.66)
  7. Calculate Interest Earned: Now we will calculate the interest earned by subtracting the initial investment from the total amount.\newlineInterest Earned = A−PA - P\newlineInterest Earned = ($1,199.66)−($700)(\$1,199.66) - (\$700)
  8. Perform Subtraction: Perform the subtraction to find the interest earned.\newlineInterest Earned ≈\approx $1,199.66−$700\$1,199.66 - \$700\newlineInterest Earned ≈\approx $499.66\$499.66

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