Dianelys deposits $6,100 every year into an account earning an annual interest rate of 5% compounded annually. How much would she have in the account after 4 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:

Question

Dianelys deposits  $6,100 every year into an account earning an annual interest rate of  5% compounded annually. How much would she have in the account after 4 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 to use in the formula. We have: d = $6,100 (the amount invested at the end of each period) i = 5% or 0.05 (the interest rate per period) n = 4 (the number of periods)Convert interest rate: Convert the percentage interest rate to a decimal. i = 5% = 5/100 = 0.05Plug values into formula: Plug the values into the compound interest formula to calculate the future value of the account. A = d * (((1 + i)^n - 1) / i) A = 6100 * (((1 + 0.05)^4 - 1) / 0.05)Calculate compound factor: Calculate the compound factor (1 + i)^n. (1 + i)^n = (1 + 0.05)^4 (1 + i)^n = 1.05^4 (1 + i)^n ≈ 1.21550625Calculate numerator: Calculate the numerator of the formula: ((1 + i)^n - 1). ((1 + i)^n - 1) ≈ 1.21550625 - 1 ((1 + i)^n - 1) ≈ 0.21550625Calculate future value: Calculate the future value of the account using the formula. A ≈ 6100 * (0.21550625 / 0.05) A ≈ 6100 * 4.310125 A ≈ 26291.7625Round to nearest dollar: Round the future value to the nearest dollar. A ≈ $26,292

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