Zachary is saving money and plans on making monthly contributions into an account earning an annual interest rate of 4.2% compounded monthly. If Zachary would like to end up with $8,000 after 21 months, how much does he need to contribute to the account every month, 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:

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Zachary is saving money and plans on making monthly contributions into an account earning an annual interest rate of  4.2% compounded monthly. If Zachary would like to end up with  $8,000 after 21 months, how much does he need to contribute to the account every month, 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:

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Identify Given Values: Identify the given values from the problem. A (future value of the account) = $8,000 n (number of periods) = 21 months i (interest rate per period) = 4.2% annual interest rate compounded monthly First, we need to convert the annual interest rate to a monthly interest rate by dividing by 12 (since there are 12 months in a year). i = 4.2% / 12 i = 0.042 / 12 i = 0.0035Convert Annual Rate: Substitute the values into the formula. We have the formula A = d * (((1 + i)^(n) - 1) / i). Now we substitute the values we have into the formula. A = $8,000 i = 0.0035 n = 21 We need to find d.Substitute Values: Solve for d using the formula. $8,000 = d * (((1 + 0.0035)^(21) - 1) / 0.0035) Now we calculate the right side of the equation step by step. First, calculate (1 + i)^n: (1 + 0.0035)^21Solve for d: Calculate the compound factor. (1 + 0.0035)^21 ≈ 1.0759 Now we subtract 1 from the compound factor. 1.0759 - 1 ≈ 0.0759Calculate Compound Factor: Divide by the interest rate per period. 0.0759 / 0.0035 ≈ 21.6857 Now we have the denominator of the formula.Divide by Interest Rate: Solve for the monthly contribution d. $8,000 = d * 21.6857 Now we divide both sides by 21.6857 to solve for d. d ≈ $8,000 / 21.6857 d ≈ 368.85Solve for Monthly Contribution: Round the monthly contribution to the nearest dollar. Zachary needs to contribute approximately $369 every month.

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