Dylan deposits $5,800 every year into an account earning an annual interest rate of 6.8% compounded annually. How much would he have in the account after 6 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

Dylan deposits  $5,800 every year into an account earning an annual interest rate of  6.8% compounded annually. How much would he have in the account after 6 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 (the amount invested at the end of each period) = $5,800 i (the interest rate per period) = 6.8% or 0.068 when converted to decimal n (the number of periods) = 6 yearsConvert Interest Rate: Convert the interest rate from a percentage to a decimal. i = 6.8% = 6.8/100 = 0.068Plug Values into Formula: Plug the values into the formula to calculate the future value of the account. A = d * (((1 + i)^n - 1) / i) A = 5800 * (((1 + 0.068)^6 - 1) / 0.068)Calculate Value Inside Parentheses: Calculate the value inside the parentheses. Calculate (1 + i)^n: (1 + 0.068)^6 = 1.068^6Calculate Exponent: Calculate the exponent part of the formula. 1.068^6 ≈ 1.4843 (rounded to four decimal places for intermediate calculations)Subtract One: Subtract 1 from the result of Step 5. 1.4843 - 1 = 0.4843Divide by i: Divide the result of Step 6 by i. 0.4843 / 0.068 ≈ 7.1250 (rounded to four decimal places for intermediate calculations)Multiply by d: Multiply the result of Step 7 by d to find the future value A. A = 5800 * 7.1250 A ≈ 41325 (rounded to the nearest dollar)

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