As always, you first need to find your effective interest rate per compounding period. Let’s assume that you were working a normal problem, not continuous compounding. The nominal yearly rate is 6% per year, and since she deposits money 24 times a year, she and the bank must have agreed to an effective rate per compounding period of 0.06/24 = 0.0025% per compounding period. We would normally use that as our effective rate for compounding, along with the equations on page 355 (old text), or page 386 (new text). The total number of compounding periods (n) would be 48 (two a month) to move the “A” 2 years into the future (excluding the first payment, which is at a non-standard time – i.e. at n = 0.)

Thus you would move the 48 values of A (two a month) to the future with F=A(F/A,i,n) + the initial non-standard deposit made today to the future with F = P(F/P,i,n).

Final answer (neglecting continuous compounding) for future value: F = A(F/A,0.0025,48) + P(F/P.0.0025,48)

However, since they are compounding continuously, you instead need to use the equations on page 358 (old text), page 390 {new text}, which are the same, but account for continuous compounding. The work is the same. Only the continuous compounding equations must instead be used to move A into a future value F, and then move the single “now” payment to F.