To calculate the annual deposit Fiona needs to make to reach a total of $400,000 in her retirement account after 25 years with an annual interest rate of 6.2%, we can use the formula for the future value of an ordinary annuity:
Future Value = Payment × [(1 + r)^n - 1] / r
Where:
- Future Value = $400,000
- Payment = Amount to be deposited each year
- r = Annual interest rate = 6.2% = 0.062
- n = Number of years = 25
Now, we can plug in the values and solve for the payment:
$400,000 = Payment × [(1 + 0.062)^25 - 1] / 0.062
$400,000 = Payment × [3.1958 - 1] / 0.062
$400,000 = Payment × 2.1958 / 0.062
$400,000 = Payment × 35.4387
Payment = $400,000 / 35.4387
Payment ≈ $11,286.42
Therefore, Fiona needs to deposit approximately $11,286.42 into her retirement account each year to reach a total of $400,000 by the time she retires after 25 years.
