A 34 -year old woman has \( \$ 388,115.00 \) in an IRA account. Due to medical concerns of a family member, she decided to make no additional contributions to the account but expect it to grow at \( 7 \% \) compounded every 4 months. How much does she expect to have in the account when she retires at age 62 ? Round value to the nearest cent. The IRA should be worth \( \$ \)

To calculate how much the IRA will be worth at retirement, we can use the compound interest formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial sum of money, which is \( \$388,115.00 \)). - \( r \) is the annual interest rate (decimal) (7% or 0.07). - \( n \) is the number of times that interest is compounded per unit year (every 4 months, or 3 times a year). - \( t \) is the time the money is invested or borrowed for, in years (from age 34 to 62, which is 28 years). Plugging in the values: - \( r = 0.07 \) - \( n = 3 \) (since interest is compounded every 4 months) - \( t = 28 \) Now substituting: \[ A = 388115 \left(1 + \frac{0.07}{3}\right)^{3 \times 28} \] Calculating: 1. Find \( \frac{0.07}{3} = 0.0233333 \). 2. Now calculate \( 3 \times 28 = 84 \). 3. Calculate \( A \): \[ A = 388115 \left(1 + 0.0233333\right)^{84} \] \[ A = 388115 \times (1.0233333)^{84} \] \[ A = 388115 \times 5.33443 \] \[ A ≈ 2,069,244.77 \] So when she retires at age 62, the IRA should be worth approximately **\$2,069,244.77**.