The value of the initial deposit is $2,960, so a1=2960. A total of 26 six-month deposits are made in the 13 years, so n=26. To find r, divide the annual interest rate by 2 to find the biannual interest rate and add 1 to represent the new biannual deposit.
r=1+0.072=1.035
Substitute a1=2960, n=26, and r=1.035 into the formula for the sum of the first n terms of a geometric series and simplify to find the value of the annuity.
S26=2960(1−1.03526)1−1.035≈122286.78
Therefore, the account has $122,286.78 after the last deposit is made.