James deposits a fixed monthly amount into an annuity account for his child's college fund. He wishes to accumulate a future value of $85,000 in 17 years. Assuming an APR of 3.8% compounded monthly, how much of the $85,000 will James ultimately deposit in the account, and how much is interest earned? Round your answers to the nearest cent, if necessary.
Formulas:
Future Value = Pmt * (((1 + r)^n - 1) / r)
Interest Earned = Future Value - Total Deposits
Answer:
To calculate the amount James will ultimately deposit in the account, we can use the formula for Future Value. Plugging in the values:
$85,000 = Pmt * (((1 + 0.038/12)^(17*12) - 1) / (0.038/12))
Solving for Pmt, we find that James will ultimately deposit approximately $41,292.67 into the account.
To calculate the interest earned, we subtract the total deposits from the future value:
Interest Earned = $85,000 - $41,292.67 = $43,707.33
Therefore, James will deposit $41,292.67 into the account, and the interest earned will be $43,707.33.