How much should Jessica have in a savings account that is earning 3.50% compounded semi-annually, if she plans to withdraw $2,150 from this account at the end of every six months for 10 years?

To determine how much Jessica should have in her savings account, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years

Given:
Principal investment (P) = unknown
Annual interest rate (r) = 3.50% = 0.035 (as a decimal)
Compounding frequency (n) = 2 (compounded semi-annually)
Time period (t) = 10 years
Withdrawal amount per period = $2,150

Now, let's calculate how much Jessica should have in her savings account by substituting the values into the formula.

Step 1: Calculate the number of compounding periods
Since interest is compounded semi-annually, and the time period is in years, we need to multiply the number of years by the compounding frequency:
n * t = 2 * 10 = 20 (compounding periods)

Step 2: Calculate the future value (A)
We know that Jessica plans to withdraw $2,150 at the end of every six months. So, within the 10-year period, she will make 20 withdrawals.
To calculate the future value, we need to subtract the sum of all the withdrawals from the total future value.

Withdrawal per period = $2,150
Total withdrawals in 10 years = 20 * $2,150 = $43,000

Now, we can calculate the future value (A) by subtracting the total withdrawals from the final amount:
A = P(1 + r/n)^(nt) - $43,000

Step 3: Rearrange the formula to find the principal investment (P)
Since we want to find the principal investment (P), we need to rearrange the formula:

P = (A + $43,000) / (1 + r/n)^(nt)

Substituting the known values into the formula, we get:

P = (A + $43,000) / (1 + 0.035/2)^(2*10)

Now, we can calculate the final answer using a calculator or spreadsheet software.