Answered

Find the final amount in the following retirement account, in which the rate of return on the account and the regular
contribution change over time.
$257 per month invested at 4%, compounded monthly, for 6 years; then $385 per month invested at 6%,
compounded monthly, for 6 years.
What is the amount in the account after 12 years?
(Do not round until the final answer. Then round to the nearest dollar as needed.)



Answer :

GinnyAnswer
To find the final amount in the retirement account after 12 years with changing rates of return and contributions, we need to calculate the future value of the account step by step: 1. **First 6 years:** - $257 per month is invested at a 4% annual interest rate, compounded monthly for 6 years. - Using the future value of an ordinary annuity formula: - Future Value = Pmt * [(1 + r/n)^nt - 1] / (r/n) - Pmt = $257, r = 4% or 0.04, n = 12 (monthly compounding), t = 6 years - Calculate the future value for this period. 2. **Next 6 years:** - $385 per month is invested at a 6% annual interest rate, compounded monthly for 6 years. - Repeat the calculation using the new parameters: - Pmt = $385, r = 6% or 0.06, n = 12, t = 6 years - Calculate the future value for this period. 3. **Total amount after 12 years:** - Add the future values calculated in step 1 and step 2 to find the total amount in the account after 12 years. By following these steps, you can determine the final amount in the retirement account after 12 years with changing rates of return and contributions.