Ayden deposits $290 every month into an account earning a monthly interest rate of 0.7%. How much would he have in the account after 13 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

Ayden deposits  $290 every month into an account earning a monthly interest rate of  0.7%. How much would he have in the account after 13 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: Monthly deposit (d) = $290 Monthly interest rate (i) = 0.7% or 0.007 (as a decimal) Number of years = 13 Number of periods (n) = 13 years * 12 months/year = 156 monthsConvert interest rate: Convert the interest rate to decimal form. 0.7% as a decimal is 0.7 / 100 = 0.007Calculate periods: Calculate the number of periods. Since Ayden deposits monthly and we are looking at a 13-year period, we multiply the number of years by the number of months in a year. n = 13 years * 12 months/year = 156 monthsUse formula for future value: Use the formula to calculate the future value of the account. A = d * (((1 + i)^(n) - 1) / i) A = $290 * (((1 + 0.007)^(156) - 1) / 0.007)Calculate future value: Calculate the future value using the values from the previous steps. A = $290 * (((1 + 0.007)^(156) - 1) / 0.007) A = $290 * (((1.007)^(156) - 1) / 0.007)Perform calculations: Perform the calculations inside the parentheses first. (1.007)^(156) - 1Calculate exponentiation: Calculate the exponentiation part of the formula. (1.007)^(156) ≈ 2.03009 (rounded to five decimal places for simplicity)Subtract from result: Subtract 1 from the result of the exponentiation. 2.03009 - 1 ≈ 1.03009Divide by interest rate: Divide the result by the interest rate. 1.03009 / 0.007 ≈ 147.15571Multiply by deposit amount: Multiply the result by the monthly deposit amount. A = $290 * 147.15571 A ≈ $42675.1559Round final answer: Round the final answer to the nearest dollar. A ≈ $42675 (to the nearest dollar)

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