Joseph is saving money and plans on making monthly contributions into an account earning a monthly interest rate of 0.75%. If Joseph would like to end up with $259,000 after 13 years, how much does he need to contribute to the account every month, 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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Joseph is saving money and plans on making monthly contributions into an account earning a monthly interest rate of  0.75%. If Joseph would like to end up with  $259,000 after 13 years, how much does he need to contribute to the account every month, 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) = $259,000 i (monthly interest rate) = 0.75% or 0.0075 when converted to decimal n (total number of periods in months) = 13 years * 12 months/year = 156 months We will use the formula A=d(((1+i)^(n)-1)/(i)) to find d, the monthly contribution.Substitute Values into Formula: Substitute the given values into the formula. A = $259,000 i = 0.0075 n = 156 Now, plug these values into the formula to solve for d.Calculate Exponent: Calculate the value inside the parentheses and the exponent. First, calculate (1+i)^n which is (1+0.0075)^156.Compute (1+0.0075)^156: Use a calculator to compute (1+0.0075)^156. (1+0.0075)^156 ≈ 3.4449 (rounded to four decimal places for simplicity)Subtract 1: Subtract 1 from the result obtained in Step 4. 3.4449 - 1 ≈ 2.4449Divide by i: Divide the result from Step 5 by i. 2.4449 / 0.0075 ≈ 325.9867Substitute into Formula: Substitute the result from Step 6 into the formula to solve for d. $259,000 = d * 325.9867 Now, solve for d by dividing both sides of the equation by 325.9867.Calculate Monthly Contribution: Calculate the monthly contribution d. d = $259,000 / 325.9867 ≈ $794.55 Since the question asks for the nearest dollar, we round this to $795.

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