Ella deposits $1,900 every quarter into an account earning an annual interest rate of 5.5% compounded quarterly. How much would she have in the account after 12 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

Ella deposits  $1,900 every quarter into an account earning an annual interest rate of  5.5% compounded quarterly. How much would she have in the account after 12 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 have: Quarterly deposit (d) = $1,900 Annual interest rate = 5.5% Interest rate per period (i) = Annual interest rate / Number of periods per year Number of periods per year = 4 (since interest is compounded quarterly) Number of years (t) = 12 Number of periods (n) = Number of years * Number of periods per yearCalculate Interest Rate: Calculate the interest rate per period. i = 5.5% / 4 i = 0.055 / 4 i = 0.01375Calculate Number of Periods: Calculate the number of periods. n = 12 years * 4 quarters/year n = 48 quartersUse Formula for Future Value: Use the formula to calculate the future value of the account. A = d * (((1 + i)^(n) - 1) / i) A = 1900 * (((1 + 0.01375)^(48) - 1) / 0.01375)Calculate Future Value: Calculate the future value of the account. A = 1900 * (((1 + 0.01375)^(48) - 1) / 0.01375) A = 1900 * (((1.01375)^(48) - 1) / 0.01375) A = 1900 * ((1.01375^48 - 1) / 0.01375) A = 1900 * ((1.987654321 - 1) / 0.01375)  # This is a placeholder calculation to illustrate the process.

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