Charlotte is saving money and plans on making monthly contributions into an account earning a monthly interest rate of 0.7%. If Charlotte would like to end up with $13,000 after 35 months, how much does she need to contribute to the account every month, 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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Charlotte is saving money and plans on making monthly contributions into an account earning a monthly interest rate of  0.7%. If Charlotte would like to end up with  $13,000 after 35 months, how much does she need to contribute to the account every month, 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. A (future value of the account) = $13,000 i (interest rate per period) = 0.7% per month, which is 0.007 in decimal form n (number of periods) = 35 months We need to find d (the amount invested at the end of each period).Plug Values into Formula: Plug the given values into the formula to solve for d. The formula is A = d * (((1 + i)^(n) - 1) / i). We have A = $13,000, i = 0.007, and n = 35.Calculate (1 + i)^n: Calculate the value of (1 + i)^n. (1 + i)^n = (1 + 0.007)^35 Use a calculator to find the value. (1 + 0.007)^35 ≈ 1.276Calculate Numerator: Calculate the numerator of the formula: ((1 + i)^(n) - 1). ((1 + i)^(n) - 1) = 1.276 - 1 ((1 + i)^(n) - 1) ≈ 0.276Calculate Denominator: Calculate the denominator of the formula: i. The denominator is simply the interest rate per period in decimal form, which is 0.007.Calculate Fraction: Calculate the entire fraction part of the formula: (((1 + i)^(n) - 1) / i). (((1 + i)^(n) - 1) / i) = 0.276 / 0.007 (((1 + i)^(n) - 1) / i) ≈ 39.429Calculate d: Calculate d using the formula A = d * (((1 + i)^(n) - 1) / i). $13,000 = d * 39.429 To find d, divide $13,000 by 39.429. d ≈ $13,000 / 39.429 d ≈ $329.49Round Monthly Contribution: Round the monthly contribution to the nearest dollar. d ≈ $329.49 is approximately $329 when rounded to the nearest dollar.

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