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7700 dollars is placed in an account with an annual interest rate of 8%. How much will be in the account after 22 years, to the nearest cent? Answer:

77007700 dollars is placed in an account with an annual interest rate of 8% 8 \% . How much will be in the account after 2222 years, to the nearest cent?\newlineAnswer:

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Q. 77007700 dollars is placed in an account with an annual interest rate of 8% 8 \% . How much will be in the account after 2222 years, to the nearest cent?\newlineAnswer:
  1. Identify values: Identify the initial principal amount, the annual interest rate, and the time period.\newlineThe initial principal amount PP is $7700\$7700, the annual interest rate rr is 8%8\% or 0.080.08 in decimal form, and the time period tt is 2222 years.
  2. Determine interest type: Determine the type of interest being applied.\newlineIf the interest is compounded annually, we will use the formula for compound interest: A=P(1+r/n)(nt)A = P(1 + r/n)^{(nt)}, where AA is the amount of money accumulated after nn years, including interest, nn is the number of times that interest is compounded per year, and tt is the time the money is invested for in years. Since the problem does not specify the compounding frequency, we will assume it is compounded annually, so n=1n = 1.
  3. Substitute into formula: Substitute the known values into the compound interest formula.\newlineUsing the values from Step 11 and assuming annual compounding from Step 22, we get:\newlineA=7700(1+0.08/1)(1×22)A = 7700(1 + 0.08/1)^{(1\times22)}
  4. Calculate accumulated amount: Calculate the amount of money accumulated after 2222 years.\newlineA=7700(1+0.08)22A = 7700(1 + 0.08)^{22}\newlineA=7700(1.08)22A = 7700(1.08)^{22}\newlineNow we need to calculate (1.08)22(1.08)^{22}.
  5. Calculate (1.08)22(1.08)^{22}: Calculate (1.08)22(1.08)^{22} using a calculator.\newline(1.08)22≈5.0226(1.08)^{22} \approx 5.0226 (rounded to four decimal places for intermediate calculations)
  6. Multiply by principal amount: Multiply the result from Step 55 by the initial principal amount.\newlineA=7700×5.0226A = 7700 \times 5.0226\newlineA≈38674.02A \approx 38674.02
  7. Round final answer: Round the final answer to the nearest cent.\newlineThe amount of money in the account after 2222 years, rounded to the nearest cent, is approximately $38,674.02\$38,674.02.

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