Nicole is saving money and plans on making quarterly contributions into an account earning an annual interest rate of 3.1% compounded quarterly. If Nicole would like to end up with $31,000 after 11 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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Nicole is saving money and plans on making quarterly contributions into an account earning an annual interest rate of  3.1% compounded quarterly. If Nicole would like to end up with  $31,000 after 11 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 Given Values: Identify the given values from the problem. A (future value of the account) = $31,000 i (interest rate per period) = 3.1% annual interest rate compounded quarterly, which is 3.1%/4 per quarter n (number of periods) = 11 years * 4 quarters/yearConvert Annual Interest Rate: Convert the annual interest rate to a quarterly interest rate. i = 3.1% per year / 4 quarters per year = 0.031 / 4 = 0.00775 per quarterCalculate Number of Periods: Calculate the number of periods (n). n = 11 years * 4 quarters/year = 44 quartersPlug Values into Formula: Plug the values into the formula to solve for d (the amount invested at the end of each period). A = d * (((1 + i)^(n) - 1) / i) $31,000 = d * (((1 + 0.00775)^(44) - 1) / 0.00775)Calculate Value Inside Parentheses: Calculate the value inside the parentheses. (1 + 0.00775)^(44) - 1 = (1.00775)^(44) - 1 = 1.414477 - 1 = 0.414477Divide by Interest Rate: Divide the result by the interest rate per period. 0.414477 / 0.00775 = 53.48361Solve for d: Solve for d by dividing the future value of the account by the result from Step 6. d = $31,000 / 53.48361 d = 579.346Round to Nearest Dollar: Round the result to the nearest dollar. d ≈ $579

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