Jose deposits $7,500 every year into an account earning an annual interest rate of 5.9% compounded annually. How much would he have in the account after 10 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

Jose deposits  $7,500 every year into an account earning an annual interest rate of  5.9% compounded annually. How much would he have in the account after 10 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 Given Values: Identify the given values from the problem. We are given: d (the amount invested at the end of each period) = $7,500 i (the interest rate per period) = 5.9% or 0.059 when converted to decimal n (the number of periods) = 10 years We will use these values in the compound interest formula to find A (the future value of the account).Convert Interest Rate: Convert the annual interest rate from a percentage to a decimal. To convert 5.9% to a decimal, divide by 100. i = 5.9% / 100 = 0.059Substitute Values in Formula: Substitute the values into the compound interest formula. Using the formula A = d * (((1 + i)^(n) - 1) / i), we substitute the values we have: A = $7,500 * (((1 + 0.059)^(10) - 1) / 0.059)Calculate Exponential Value: Calculate the value inside the parentheses (1 + i)^(n). (1 + 0.059)^(10) = (1.059)^(10) Now, calculate the exponentiation. (1.059)^(10) ≈ 1.77729 (rounded to five decimal places for precision in further calculations)Subtract One: Continue with the formula by subtracting 1 from the result obtained in Step 4. 1.77729 - 1 = 0.77729Divide by Interest Rate: Divide the result from Step 5 by the interest rate i. 0.77729 / 0.059 ≈ 13.17559Multiply by Amount: Multiply the result from Step 6 by the amount invested at the end of each period d. $7,500 * 13.17559 ≈ $98,817.42Round Final Result: Round the final result to the nearest dollar. The future value of the account, rounded to the nearest dollar, is approximately $98,817.

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