Mariam is saving money and plans on making quarterly contributions into an account earning an annual interest rate of 5% compounded quarterly. If Mariam would like to end up with $8,000 after 3 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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Mariam is saving money and plans on making quarterly contributions into an account earning an annual interest rate of  5% compounded quarterly. If Mariam would like to end up with  $8,000 after 3 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. Future value of the account, A = $8,000 Annual interest rate = 5% Number of years = 3 Since the interest is compounded quarterly, there are 4 periods per year. Therefore, the number of periods, n = 3 years * 4 quarters/year = 12 quarters The interest rate per period, i = (5% annual interest rate) / 4 quarters = 1.25% per quarter or 0.0125 in decimal form.Substitute Values into Formula: Substitute the given values into the formula to solve for d, the amount invested at the end of each period. We have the formula A = d * (((1 + i)^(n) - 1) / i) Substituting the values, we get: $8,000 = d * (((1 + 0.0125)^(12) - 1) / 0.0125)Calculate Value Inside Parentheses: Calculate the value inside the parentheses. Calculate (1 + i)^n: (1 + 0.0125)^12Perform Exponentiation: Perform the exponentiation. (1 + 0.0125)^12 ≈ 1.160Continue Calculation of Formula: Continue with the calculation of the formula. $8,000 = d * ((1.160 - 1) / 0.0125)Calculate Numerator of Fraction: Calculate the numerator of the fraction. 1.160 - 1 = 0.160Calculate Denominator of Fraction: Calculate the denominator of the fraction. Now we have: $8,000 = d * (0.160 / 0.0125)Perform Division: Perform the division to solve for d. $8,000 = d * (12.8)Isolate d: Isolate d to solve for the quarterly contribution. d = $8,000 / 12.8Calculate Value of d: Calculate the value of d. d ≈ $625Round Value of d: Round the value of d to the nearest dollar. Mariam needs to contribute approximately $625 every quarter.

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