Tanisha is saving money and plans on making quarterly contributions into an account earning an annual interest rate of 6.7% compounded quarterly. If Tanisha would like to end up with $96,000 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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Tanisha is saving money and plans on making quarterly contributions into an account earning an annual interest rate of  6.7% compounded quarterly. If Tanisha would like to end up with  $96,000 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) = $96,000 i (interest rate per period) = 6.7% annual interest rate compounded quarterly, which means i = 6.7% / 4 = 0.067 / 4 per quarter n (number of periods) = 11 years * 4 quarters/year = 44 quarters Now, we can use these values to find d (the amount invested at the end of each period).Convert Interest Rate: Convert the annual interest rate to a quarterly interest rate. i = 0.067 / 4 = 0.01675 This is the interest rate per quarter.Calculate Number of Periods: Calculate the number of periods (n). n = 11 years * 4 quarters/year = 44 quartersCalculate (1+i)^n: Use the formula A = d(((1+i)^(n)-1)/(i)) to find d. First, calculate (1+i)^n. (1+i)^n = (1 + 0.01675)^44Calculate (1+i)^n: Calculate (1+i)^n using a calculator. (1 + 0.01675)^44 ≈ 2.03009Calculate ((1+i)^n - 1): Calculate ((1+i)^n - 1). ((1+i)^n - 1) ≈ 2.03009 - 1 = 1.03009Calculate Denominator: Calculate the denominator of the formula, which is i. i = 0.01675Calculate Right Side: Calculate the entire right side of the formula, which is (((1+i)^(n)-1)/(i)). (((1+i)^(n)-1)/(i)) ≈ 1.03009 / 0.01675 ≈ 61.5493Solve for d: Solve for d using the formula A = d(((1+i)^(n)-1)/(i)). $96,000 = d * 61.5493 Now, divide both sides by 61.5493 to find d. d ≈ $96,000 / 61.5493Calculate d: Calculate d using a calculator. d ≈ $96,000 / 61.5493 ≈ $1559.68 Since we need to round to the nearest dollar, d ≈ $1560.

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