A 39-year old woman has $$ \$ 321,105.00 $$ 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 $$ 6.5 \% $$ compounded every 4 months. How much does she expect to have in the account when she retires at age 67 ?

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To calculate the future value of the IRA account when the woman retires at age 67, we can use the formula for compound interest:

$$
A = P \left(1 + \frac{r}{n}\right)^{nt}
$$

Where:
- $$ A $$ is the amount of money accumulated after n years, including interest.
- $$ P $$ is the principal amount (the initial amount of money).
- $$ r $$ is the annual interest rate (decimal).
- $$ n $$ is the number of times that interest is compounded per year.
- $$ t $$ is the number of years the money is invested or borrowed for.

Given:
- $$ P = 321,105 $$
- $$ r = 6.5\% = 0.065 $$
- The interest is compounded every 4 months, so $$ n = 3 $$ (since there are 3 compounding periods in a year).
- The woman is currently 39 years old and plans to retire at 67, so $$ t = 67 - 39 = 28 $$ years.

Now we can plug in the values into the formula:

$$
A = 321,105 \left(1 + \frac{0.065}{3}\right)^{3 \times 28}
$$

Calculating $$ \frac{0.065}{3} $$:

$$
\frac{0.065}{3} \approx 0.0216667
$$

Now, calculate $$ 1 + 0.0216667 $$:

$$
1 + 0.0216667 \approx 1.0216667
$$

Next, calculate $$ 3 \times 28 = 84 $$.

Now we can calculate $$ A $$:

$$
A = 321,105 \left(1.0216667\right)^{84}
$$

Calculating $$ (1.0216667)^{84} $$:

$$
(1.0216667)^{84} \approx 5.155
$$

Now, multiply this by the principal:

$$
A \approx 321,105 \times 5.155 \approx 1,655,000.78
$$

Thus, the expected amount in the account when she retires at age 67 is approximately:

$$
\boxed{1,655,000.78}
$$
The woman expects to have approximately \$1,655,000.78 in her IRA account when she retires at age 67.

A 39-year old woman has 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 compounded
every 4 months. How much does she expect to have in the account when she retires at age 67 ?

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A 39-year old woman has 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 compounded every 4 months. How much does she expect to have in the account when she retires at age 67 ?