Charlotte is saving money and plans on making monthly contributions into an account earning an annual interest rate of 3% compounded monthly. If Charlotte would like to end up with $61,000 after 9 years, how much does she 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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Charlotte is saving money and plans on making monthly contributions into an account earning an annual interest rate of  3% compounded monthly. If Charlotte would like to end up with  $61,000 after 9 years, how much does she 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) = $61,000 n (number of periods) = 9 years * 12 months/year = 108 months i (interest rate per period) = 3% per year / 12 months = 0.03 / 12Substitute Values into Formula: Substitute the given values into the formula. A = d * (((1 + i)^(n) - 1) / i) $61,000 = d * (((1 + 0.03/12)^(108) - 1) / (0.03/12))Calculate Value Inside Parentheses: Calculate the value inside the parentheses (1 + i)^(n). (1 + 0.03/12)^(108) = (1 + 0.0025)^(108)Calculate Value of (1 + i)^(n): Calculate the value of (1 + i)^(n). (1 + 0.0025)^(108) ≈ 1.349858807576003Calculate Numerator of Formula: Calculate the numerator of the formula (((1 + i)^(n) - 1). 1.349858807576003 - 1 ≈ 0.349858807576003Calculate Denominator of Formula: Calculate the denominator of the formula (i). 0.03/12 = 0.0025Calculate Entire Fraction: Calculate the entire fraction of the formula (((1 + i)^(n) - 1) / i). 0.349858807576003 / 0.0025 ≈ 139.9435230304012Solve for d: Solve for d (the amount invested at the end of each period). $61,000 = d * 139.9435230304012 d = $61,000 / 139.9435230304012Calculate Value of d: Calculate the value of d. d ≈ $61,000 / 139.9435230304012 ≈ $435.62

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