Madeline deposits $5,800 every year into an account earning an annual interest rate of 5.2% compounded annually. How much would she have in the account after 15 years, 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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Madeline deposits  $5,800 every year into an account earning an annual interest rate of  5.2% compounded annually. How much would she have in the account after 15 years, 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 variables: Identify the variables from the problem. We are given: d = $5,800 (the amount invested at the end of each period) i = 5.2% or 0.052 (the interest rate per period) n = 15 (the number of periods) We need to find A, the future value of the account after n periods.Convert interest rate: Convert the percentage interest rate to a decimal. i = 5.2% = 5.2/100 = 0.052Plug values into formula: Plug the values into the compound interest formula. A = d * (((1 + i)^n - 1) / i) A = $5,800 * (((1 + 0.052)^15 - 1) / 0.052)Calculate compound factor: Calculate the compound factor (1 + i)^n. (1 + i)^n = (1 + 0.052)^15 (1 + i)^n ≈ 1.052^15 (1 + i)^n ≈ 2.1133137 (rounded to 7 decimal places for precision)Calculate numerator: Calculate the numerator of the formula: ((1 + i)^n - 1). ((1 + i)^n - 1) ≈ 2.1133137 - 1 ((1 + i)^n - 1) ≈ 1.1133137Divide by interest rate: Divide the result from Step 5 by the interest rate i. (1.1133137) / 0.052 ≈ 21.4094952 (rounded to 7 decimal places for precision)Multiply by amount: Multiply the result from Step 6 by the amount invested at the end of each period d. A ≈ $5,800 * 21.4094952 A ≈ $124,174.8716Round future value: Round the future value of the account to the nearest dollar. A ≈ $124,175

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