Question

You just turned 25 years old and want to retire when you turn 65. You plan to put $4,600 every year into a ROTH IRA, a retirement account from which you can withdraw money after retirement without having to pay any taxes. You expect to earn a return of 6% on your investments every year. Part 1 How much money can you expect to have at age 65 if you make your first annual deposit now and your last one on the day you turn 64?

Answer 1

Using the formula for the future value of an annuity, a student making annual deposits of $4,600 into a Roth IRA can expect to have approximately $711,903.82 by age 65, assuming a 6% annual return and no withdrawals.

Step-by-step explanation:

The student wants to know how much money they can expect to have at age 65 if they make their first annual deposit of $4,600 into a Roth IRA now and their last one on the day they turn 64, with an expected annual return of 6%. To calculate this, we need to use the formula for the future value of an annuity:

`Future Value = Pmt × 【((1 + r)^n - 1) / r】`

Where:

• ‘Pmt’ is the annual payment/deposit ($4,600)
• ‘r’ is the annual interest rate (0.06)
• ‘n’ is the number of years the money is deposited (40)

Plugging in the values:

`Future Value = $4,600 × 【((1 + 0.06)^40 - 1) / 0.06】`

`Future Value = $4,600 × 【(1.06^40 - 1) / 0.06】`

Future Value = $4,600 × 【(10.2857 - 1) / 0.06】

Future Value = $4,600 × 154.7617

Future Value = $711,903.82

Therefore, if the student makes annual deposits of $4,600 every year until they turn 64, they can expect to have approximately $711,903.82 by the age of 65, assuming a 6% annual return on investment and that they do not withdraw any money before that time.