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Abdoulaye deposits $310 every month into an account earning a monthly interest rate of 0.475%. How much would he have in the account after 6 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:

Abdoulaye deposits $310 \$ 310 every month into an account earning a monthly interest rate of 0.475% 0.475 \% . How much would he have in the account after 66 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. Abdoulaye deposits $310 \$ 310 every month into an account earning a monthly interest rate of 0.475% 0.475 \% . How much would he have in the account after 66 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.\newlineWe have:\newlineMonthly deposit dd = $310\$310\newlineMonthly interest rate ii = 0.475%0.475\% or 0.004750.00475 in decimal form\newlineNumber of periods nn = 66 months\newlineWe will use these values to calculate the future value of the account AA using the given formula.
  2. Convert Interest Rate: Convert the interest rate from a percentage to a decimal.\newlineTo convert the interest rate to a decimal, we divide by 100100.\newlinei=0.475%/100=0.00475i = 0.475\% / 100 = 0.00475
  3. Plug Values into Formula: Plug the values into the formula to calculate the future value of the account.\newlineUsing the formula A=d×((1+i)n−1)/iA = d \times \left(\left(1 + i\right)^{n} - 1\right) / i, we substitute the values we have:\newlineA=310×((1+0.00475)6−1)/0.00475A = 310 \times \left(\left(1 + 0.00475\right)^{6} - 1\right) / 0.00475
  4. Calculate Future Value: Calculate the future value of the account.\newlineFirst, calculate the compound factor (1+i)n(1 + i)^n:\newline(1+0.00475)6≈1.028689(1 + 0.00475)^6 \approx 1.028689\newlineNext, subtract 11 from the compound factor:\newline1.028689−1≈0.0286891.028689 - 1 \approx 0.028689\newlineNow, divide by the interest rate ii:\newline0.028689/0.00475≈6.0355790.028689 / 0.00475 \approx 6.035579\newlineFinally, multiply by the monthly deposit dd:\newline310×6.035579≈1871.02949310 \times 6.035579 \approx 1871.02949
  5. Round to Nearest Dollar: Round the future value to the nearest dollar.\newlineSince we need to round to the nearest dollar, we round 1871.029491871.02949 to $1871\$1871.

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