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Chloe deposits $750 every month into an account earning a monthly interest rate of 0.4%. How much would she have in the account after 3 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:

Chloe deposits $750 \$ 750 every month into an account earning a monthly interest rate of 0.4% 0.4 \% . How much would she have in the account after 33 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. Chloe deposits $750 \$ 750 every month into an account earning a monthly interest rate of 0.4% 0.4 \% . How much would she have in the account after 33 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 Given Values: Identify the given values from the problem.\newlineWe are given:\newlineMonthly deposit dd = $750\$750\newlineMonthly interest rate ii = 0.4%0.4\% or 0.0040.004 (as a decimal)\newlineNumber of periods nn = 33 years ∗12* 12 months/year = 3636 months\newlineWe will use these values in the formula provided to calculate the future value of the account.
  2. Convert Interest Rate: Convert the monthly interest rate from a percentage to a decimal.\newlineTo do this, divide the interest rate by 100100.\newlinei=0.4%100=0.004i = \frac{0.4\%}{100} = 0.004
  3. Calculate Future Value: Calculate the future value (AA) using the formula.\newlineA=d×((1+i)n−1i)A = d \times \left(\frac{(1 + i)^{n} - 1}{i}\right)\newlineSubstitute the given values into the formula.\newlineA=750×((1+0.004)36−10.004)A = 750 \times \left(\frac{(1 + 0.004)^{36} - 1}{0.004}\right)
  4. Calculate Value Inside: Calculate the value inside the parentheses.\newlineCalculate (1+i)n(1 + i)^n.\newline(1+0.004)36(1 + 0.004)^{36}
  5. Perform Exponentiation: Perform the exponentiation.\newline(1+0.004)36≈1.00436≈1.154243(1 + 0.004)^{36} \approx 1.004^{36} \approx 1.154243
  6. Continue Calculation: Continue with the formula calculation.\newlineA=750×((1.154243−1)/0.004)A = 750 \times ((1.154243 - 1) / 0.004)
  7. Subtract One: Subtract 11 from the result of the exponentiation.\newline1.154243−1=0.1542431.154243 - 1 = 0.154243
  8. Divide by Interest Rate: Divide the result by the interest rate. 0.154243/0.004=38.560750.154243 / 0.004 = 38.56075
  9. Multiply by Deposit: Multiply by the monthly deposit amount. A=750×38.56075A = 750 \times 38.56075
  10. Calculate Final Value: Calculate the final future value.\newlineA≈750×38.56075≈28920.5625A \approx 750 \times 38.56075 \approx 28920.5625
  11. Round Future Value: Round the future value to the nearest dollar.\newlineA≈$28921A \approx \$28921

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