Christopher is saving money and plans on making monthly contributions into an account earning a monthly interest rate of 0.5%. If Christopher would like to end up with $29,000 after 12 years, how much does he 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:

Question

Christopher is saving money and plans on making monthly contributions into an account earning a monthly interest rate of  0.5%. If Christopher would like to end up with  $29,000 after 12 years, how much does he 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:

Bytelearn · Accepted Answer

Identify Given Values: Identify the given values from the problem. A (future value of the account) = $29,000 i (interest rate per period) = 0.5% per month = 0.005 (as a decimal) n (number of periods) = 12 years * 12 months/year = 144 months Now we can use these values in the formula provided.Plug Values into Formula: Plug the values into the formula to solve for d (the amount invested at the end of each period). A = d * (((1 + i)^(n) - 1) / i) $29,000 = d * (((1 + 0.005)^(144) - 1) / 0.005) We need to calculate the right side of the equation to find the value of d.Calculate Compound Factor: Calculate the compound factor. (1 + i)^(n) = (1 + 0.005)^(144) Calculate the power using a calculator. (1 + 0.005)^(144) ≈ 2.0398873Calculate Numerator: Calculate the numerator of the fraction. ((1 + i)^(n) - 1) = 2.0398873 - 1 The numerator is ≈ 1.0398873Divide by Interest Rate: Divide the numerator by the interest rate i. (1.0398873) / 0.005 = 207.97746Solve for d: Solve for d by dividing A by the result from Step 5. $29,000 / 207.97746 ≈ 139.456 Since we need to find the monthly contribution to the nearest dollar, we round this to $139.

Full solution

More problems from Compound interest

Related topics