The solution to this problem is relatively straightforward. To find out how much money will be in the account after 13 years, first we need to calculate the interest rate compounded annually over that time period. Compound interest is calculated by multiplying the initial principal (in this case $2900) by one plus the annual interest rate (9%) raised to a power equal to the number of years for which it has been invested (13).

Using an online calculator or spreadsheet, we can then solve for this equation: 2900 * 1.09^13 = 5825.94

This means that if $2,900 were placed in an account with an annual interest rate of 9%, after 13 years there would be $5,825.94 in the account to the nearest cent. This amount does not include any additional contributions or withdrawals from the account during those 13 years – it only reflects what would remain if left untouched at a fixed 9% compound annual interest rate over a period of 13 years.

It’s important to note that compound interest works best when left alone without undue interference from frequent deposits and withdrawals; such activity will reduce overall gains due to added required paperwork and fees which may make compounding more expensive than its simple counterpart. That said, investments with compounding can still yield impressive returns when managed properly and left intact over long periods of time – as demonstrated above!