Josue is saving money and plans on making quarterly contributions into an account earning a quarterly interest rate of 1.875%. If Josue would like to end up with $95,000 after 15 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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Josue is saving money and plans on making quarterly contributions into an account earning a quarterly interest rate of  1.875%. If Josue would like to end up with  $95,000 after 15 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) = $95,000 i (interest rate per period) = 1.875% or 0.01875 when converted to decimal n (number of periods) = 15 years * 4 quarters/year = 60 quarters Now we can use these values in the formula provided.Substitute Values into Formula: Substitute the given values into the formula. We have the formula A = d * (((1 + i)^(n) - 1) / i), where A is the future value, d is the amount invested each period, i is the interest rate per period, and n is the number of periods. Let's plug in the values: $95,000 = d * (((1 + 0.01875)^(60) - 1) / 0.01875)Calculate Compound Factor: Calculate the compound factor. First, calculate (1 + i)^n: (1 + 0.01875)^60 Now, use a calculator to find the value.Continue Calculation: Continue the calculation from the previous step. Using a calculator, we find: (1 + 0.01875)^60 ≈ 2.45489 Now we can update our equation: $95,000 = d * ((2.45489 - 1) / 0.01875)Simplify Equation: Simplify the equation further. Subtract 1 from 2.45489: 2.45489 - 1 = 1.45489 Now, divide by the interest rate: 1.45489 / 0.01875 ≈ 77.59413 Update the equation with this value: $95,000 = d * 77.59413Solve for Amount Invested: Solve for d, the amount invested each period. To find d, divide the future value by the compound factor: d = $95,000 / 77.59413 Use a calculator to find d.Calculate and Round Value: Calculate the value of d and round to the nearest dollar. Using a calculator, we find: d ≈ $95,000 / 77.59413 ≈ $1224.14 Since we need to round to the nearest dollar, d ≈ $1224.

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