Rashaad is saving money and plans on making monthly contributions into an account earning an annual interest rate of 8.4% compounded monthly. If Rashaad would like to end up with $75,000 after 8 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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Rashaad is saving money and plans on making monthly contributions into an account earning an annual interest rate of  8.4% compounded monthly. If Rashaad would like to end up with  $75,000 after 8 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) = $75,000 i (monthly interest rate) = 8.4% annual interest rate / 12 months = 0.7% per month = 0.007 (as a decimal) n (total number of periods) = 8 years * 12 months/year = 96 months Now, we can use these values in the formula provided.Substitute Values into Formula: Substitute the given values into the formula. A = d * (((1 + i)^(n) - 1) / i) $75,000 = d * (((1 + 0.007)^(96) - 1) / 0.007) We need to solve for d, which represents the monthly contribution.Calculate Inside Parentheses: Calculate the value inside the parentheses. (1 + 0.007)^(96) - 1 First, calculate (1 + 0.007)^(96). 1.007^(96) ≈ 2.039898 (using a calculator) Now, subtract 1 from the result. 2.039898 - 1 ≈ 1.039898Divide by Interest Rate: Divide the result by the interest rate per period. 1.039898 / 0.007 ≈ 148.5568571Solve for Monthly Contribution: Solve for d by dividing the future value of the account by the result from Step 4. $75,000 / 148.5568571 ≈ $504.96 Rashaad needs to contribute approximately $504.96 each month.Round Monthly Contribution: Round the monthly contribution to the nearest dollar. Rashaad needs to contribute approximately $505 each month when rounded to the nearest dollar.

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