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Miguel deposits $470 every month into an account earning an annual interest rate of 8.1% compounded monthly. How much would he have in the account after 30 months, 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:

Miguel deposits $470 \$ 470 every month into an account earning an annual interest rate of 8.1% 8.1 \% compounded monthly. How much would he have in the account after 3030 months, 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. Miguel deposits $470 \$ 470 every month into an account earning an annual interest rate of 8.1% 8.1 \% compounded monthly. How much would he have in the account after 3030 months, 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.\newlined=$470d = \$470 (the amount invested at the end of each period)\newlinei=8.1%i = 8.1\% annual interest rate, which needs to be converted to a monthly rate by dividing by 1212.\newlinen=30n = 30 (the number of periods, which are months in this case)
  2. Convert interest rate: Convert the annual interest rate to a monthly interest rate. \newlinei=8.1% per year12 months per yeari = \frac{8.1\% \text{ per year}}{12 \text{ months per year}}\newlinei=0.08112i = \frac{0.081}{12}\newlinei=0.00675i = 0.00675 (monthly interest rate)
  3. Calculate future value: Use the formula to calculate the future value of the account after nn periods.A=d×((1+i)n−1i)A = d \times \left(\frac{(1 + i)^{n} - 1}{i}\right)
  4. Plug values and calculate: Plug the values into the formula and calculate the future value.\newlineA=470×((1+0.00675)30−1)/0.00675A = 470 \times \left(\left(1 + 0.00675\right)^{30} - 1\right) / 0.00675
  5. Calculate exponent: Calculate the value inside the parentheses and the exponent.\newline(1+0.00675)30=1.0067530(1 + 0.00675)^{30} = 1.00675^{30}
  6. Continue formula calculation: Calculate the exponent.\newline1.0067530≈1.221391.00675^{30} \approx 1.22139
  7. Calculate numerator: Continue with the formula calculation.\newlineA=470×((1.22139−1)/0.00675)A = 470 \times ((1.22139 - 1) / 0.00675)
  8. Calculate future value: Calculate the numerator of the fraction.\newline1.22139−1=0.221391.22139 - 1 = 0.22139
  9. Round to nearest dollar: Calculate the future value AA.A=470×(0.22139/0.00675)A = 470 \times (0.22139 / 0.00675)A≈470×32.80593A \approx 470 \times 32.80593A≈15418.7851A \approx 15418.7851
  10. Round to nearest dollar: Calculate the future value AA.A=470×(0.22139/0.00675)A = 470 \times (0.22139 / 0.00675)A≈470×32.80593A \approx 470 \times 32.80593A≈15418.7851A \approx 15418.7851Round the future value to the nearest dollar.A≈$(15419)A \approx \$(15419)

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