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Natalie deposits $320 every month into an account earning an annual interest rate of 9% compounded monthly. How much would she have in the account after 4 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:

Natalie deposits $320 \$ 320 every month into an account earning an annual interest rate of 9% 9 \% compounded monthly. How much would she have in the account after 44 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. Natalie deposits $320 \$ 320 every month into an account earning an annual interest rate of 9% 9 \% compounded monthly. How much would she have in the account after 44 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 are given:\newlined=$320d = \$320 (monthly deposit)\newlinei=9%i = 9\% annual interest rate, which needs to be converted to a monthly rate.\newlinen=4n = 4 years, but since the interest is compounded monthly, we need to convert this to the number of months.
  2. Convert Interest Rate: Convert the annual interest rate to a monthly interest rate.\newlineii (monthly interest rate) = annual interest rate / number of periods per year\newlinei=9%12i = \frac{9\%}{12}\newlinei=0.0912i = \frac{0.09}{12}\newlinei=0.0075i = 0.0075
  3. Convert Years to Months: Convert the number of years to the number of periods (months).\newlinenn (number of periods) = years\text{years} ∗* number of periods per year\text{number of periods per year}\newlinen=4×12n = 4 \times 12\newlinen=48n = 48
  4. Calculate Future Value: Use the formula to calculate the future value of the account.\newlineA=d×((1+i)n−1i)A = d \times \left(\frac{(1 + i)^{n} - 1}{i}\right)\newlineA=320×((1+0.0075)48−10.0075)A = 320 \times \left(\frac{(1 + 0.0075)^{48} - 1}{0.0075}\right)
  5. Calculate Future Value: Calculate the future value of the account.\newlineA=320×((1+0.0075)48−1)/0.0075A = 320 \times \left(\left(1 + 0.0075\right)^{48} - 1\right) / 0.0075\newlineA=320×((1.0075)48−1)/0.0075A = 320 \times \left(\left(1.0075\right)^{48} - 1\right) / 0.0075\newlineA=320×(1.432364654−1)/0.0075A = 320 \times \left(1.432364654 - 1\right) / 0.0075\newlineA=320×(0.432364654/0.0075)A = 320 \times \left(0.432364654 / 0.0075\right)\newlineA=320×57.64862053A = 320 \times 57.64862053\newlineA=18447.55857A = 18447.55857
  6. Round to Nearest Dollar: Round the future value to the nearest dollar.\newlineA≈$(18,448)A \approx \$(18,448)

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