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6400 dollars is placed in an account with an annual interest rate of 6.25%. How much will be in the account after 20 years, to the nearest cent? Answer:

64006400 dollars is placed in an account with an annual interest rate of 6.25% 6.25 \% . How much will be in the account after 2020 years, to the nearest cent?\newlineAnswer:

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Q. 64006400 dollars is placed in an account with an annual interest rate of 6.25% 6.25 \% . How much will be in the account after 2020 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 $6400\$6400, the annual interest rate rr is 6.25%6.25\%, and the time period tt is 2020 years.
  2. Convert rate to decimal: Convert the annual interest rate from a percentage to a decimal.\newlineTo convert the rate to a decimal, divide by 100100.\newliner=6.25%100=0.0625r = \frac{6.25\%}{100} = 0.0625
  3. Use compound interest formula: Determine the formula to calculate the future value of the investment using compound interest.\newlineThe formula for compound interest is 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, PP is the principal amount, rr is the annual interest rate (decimal), nn is the number of times that interest is compounded per year, and tt is the time the money is invested for in years.
  4. Assume compounding frequency: Since the problem does not specify the compounding frequency, assume that it is compounded annually n=1n = 1.n=1n = 1 (compounded annually)
  5. Substitute values into formula: Substitute the values into the compound interest formula to calculate the future value. \newlineA=6400(1+0.0625/1)(1×20)A = 6400(1 + 0.0625/1)^{(1\times20)}
  6. Simplify and calculate exponent: Simplify the expression inside the parentheses and then calculate the exponent.\newlineA=6400(1+0.0625)20A = 6400(1 + 0.0625)^{20}\newlineA=6400(1.0625)20A = 6400(1.0625)^{20}
  7. Calculate future value: Calculate the future value using the simplified formula.\newlineA=6400×(1.0625)20A = 6400 \times (1.0625)^{20}\newlineA=6400×3.34885A = 6400 \times 3.34885 (rounded to five decimal places)\newlineA=21432.64A = 21432.64 (rounded to the nearest cent)
  8. Check for errors: Check the calculation for any mathematical errors.\newlineRe-evaluate the expression to ensure that there are no errors in the calculation.\newlineA=6400×(1.0625)20A = 6400 \times (1.0625)^{20}\newlineA=6400×3.34885A = 6400 \times 3.34885\newlineA=21432.64A = 21432.64\newlineThe calculation appears to be correct.

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