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Ethan deposits $100 every quarter into an account earning a quarterly interest rate of 0.825%. How much would he have in the account after 11 years, to the nearest dollar? Use the following formula to determine your answer. A=d(((1+i)^(n)-1)/(i)) A= the future value of the account after n periods d= the amount invested at the end of each period i= the interest rate per period n= the number of periods Answer:

Ethan deposits $100 \$ 100 every quarter into an account earning a quarterly interest rate of 0.825% 0.825 \% . How much would he have in the account after 1111 years, to the nearest dollar? Use the following formula to determine your answer.\newlineA=d((1+i)n−1i) A=d\left(\frac{(1+i)^{n}-1}{i}\right) \newlineA= A= the future value of the account after n n periods\newlined= d= the amount invested at the end of each period\newlinei= i= the interest rate per period\newlinen= n= the number of periods\newlineAnswer:

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Q. Ethan deposits $100 \$ 100 every quarter into an account earning a quarterly interest rate of 0.825% 0.825 \% . How much would he have in the account after 1111 years, to the nearest dollar? Use the following formula to determine your answer.\newlineA=d((1+i)n−1i) A=d\left(\frac{(1+i)^{n}-1}{i}\right) \newlineA= A= the future value of the account after n n periods\newlined= d= the amount invested at the end of each period\newlinei= i= the interest rate per period\newlinen= n= the number of periods\newlineAnswer:
  1. Identify variables: Identify the variables from the problem.\newlineWe have:\newlined=$100d = \$100 (the amount invested at the end of each period)\newlinei=0.825%i = 0.825\% per quarter (the interest rate per period)\newlinen=11 years×4 quarters/year=44 quartersn = 11 \text{ years} \times 4 \text{ quarters/year} = 44 \text{ quarters} (the number of periods)
  2. Convert interest rate: Convert the interest rate from a percentage to a decimal. i=0.825%=0.825100=0.00825i = 0.825\% = \frac{0.825}{100} = 0.00825
  3. Calculate future value: Use the formula to calculate the future value of the account. A=d×((1+i)n−1i)A = d \times \left(\frac{(1 + i)^{n} - 1}{i}\right)
  4. Plug values and calculate: Plug the values into the formula and calculate the future value. \newlineA=100×((1+0.00825)44−1)/0.00825A = 100 \times \left(\left(1 + 0.00825\right)^{44} - 1\right) / 0.00825
  5. Calculate exponentiation: Calculate the value inside the parentheses and the exponentiation.\newline(1+0.00825)44=1.0082544(1 + 0.00825)^{44} = 1.00825^{44}
  6. Calculate future value: Calculate the exponentiation using a calculator.\newline1.0082544≈1.4323861.00825^{44} \approx 1.432386
  7. Calculate numerator: Continue with the formula calculation.\newlineA=100×(1.432386−10.00825)A = 100 \times \left(\frac{1.432386 - 1}{0.00825}\right)
  8. Calculate future value: Calculate the numerator of the fraction.\newline1.432386−1=0.4323861.432386 - 1 = 0.432386
  9. Finish calculation: Calculate the future value of the account.\newlineA=100×(0.432386/0.00825)A = 100 \times (0.432386 / 0.00825)
  10. Round final answer: Finish the calculation.\newlineA≈100×52.41284848A \approx 100 \times 52.41284848\newlineA≈5241.284848A \approx 5241.284848
  11. Round final answer: Finish the calculation.\newlineA≈100×52.41284848A \approx 100 \times 52.41284848\newlineA≈5241.284848A \approx 5241.284848Round the final answer to the nearest dollar.\newlineA≈$(5241)A \approx \$(5241)

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