Francisco is saving money and plans on making quarterly contributions into an account earning a quarterly interest rate of 1.45%. If Francisco would like to end up with $48,000 after 12 years, how much does he 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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Francisco is saving money and plans on making quarterly contributions into an account earning a quarterly interest rate of  1.45%. If Francisco would like to end up with  $48,000 after 12 years, how much does he 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) = $48,000 i (interest rate per period) = 1.45% or 0.0145 when converted to decimal n (number of periods) = 12 years * 4 quarters/year = 48 quarters We will use these values in the formula provided.Plug Values into Formula: Plug the given values into the formula to solve for d (the amount invested at the end of each period). The formula is A = d * (((1 + i)^(n) - 1) / i). We have A = $48,000, i = 0.0145, and n = 48.Calculate (1 + i)^n: Calculate the value inside the parentheses, (1 + i)^n. (1 + i)^n = (1 + 0.0145)^48 Use a calculator to find the value. (1 + 0.0145)^48 ≈ 1.9996Calculate ((1 + i)^n - 1): Calculate the numerator of the fraction, ((1 + i)^n - 1). ((1 + i)^n - 1) = 1.9996 - 1 ((1 + i)^n - 1) ≈ 0.9996Calculate Entire Fraction: Calculate the entire fraction, (((1 + i)^n - 1) / i). (((1 + i)^n - 1) / i) = 0.9996 / 0.0145 (((1 + i)^n - 1) / i) ≈ 68.9379Solve for d: Solve for d using the formula A = d * (((1 + i)^n - 1) / i). $48,000 = d * 68.9379 Now, divide both sides by 68.9379 to solve for d. d = $48,000 / 68.9379 d ≈ $696.15Round to Nearest Dollar: Round the result to the nearest dollar. d ≈ $696.15 rounds to $696.

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