Audrey is saving money and plans on making quarterly contributions into an account earning an annual interest rate of 3.8% compounded quarterly. If Audrey would like to end up with $6,000 after 8 years, how much does she need to contribute to the account every quarter, 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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Audrey is saving money and plans on making quarterly contributions into an account earning an annual interest rate of  3.8% compounded quarterly. If Audrey would like to end up with  $6,000 after 8 years, how much does she need to contribute to the account every quarter, 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 values: Identify the given values from the problem. A (future value of the account) = $6,000 i (interest rate per period) = 3.8% annual interest rate compounded quarterly, which is 3.8%/4 per quarter n (number of periods) = 8 years with quarterly contributions, which is 8 * 4 quarters per yearConvert interest rate: Convert the annual interest rate to a quarterly interest rate. i = 3.8% per year / 4 quarters per year = 0.038 / 4 = 0.0095 per quarterCalculate total periods: Calculate the total number of periods. n = 8 years * 4 quarters per year = 32 quartersUse formula for amount: Use the formula to find the amount invested at the end of each period (d). A = d * (((1 + i)^(n) - 1) / i) $6,000 = d * (((1 + 0.0095)^(32) - 1) / 0.0095)Calculate inside parentheses: Calculate the value inside the parentheses. (1 + 0.0095)^(32) - 1 = (1.0095)^(32) - 1Calculate exponentiation: Calculate the exponentiation. (1.0095)^(32) ≈ 1.349858807576003Subtract from result: Subtract 1 from the result of the exponentiation. 1.349858807576003 - 1 ≈ 0.349858807576003Divide by interest rate: Divide the result by the interest rate per period. 0.349858807576003 / 0.0095 ≈ 36.82724395326347Solve for d: Solve for d by dividing the future value of the account by the result from the previous step. $6,000 / 36.82724395326347 ≈ 162.974Round result: Round the result to the nearest dollar. d ≈ $163

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