For part (a) you forgot to multiply the first part (The 2 years of $12 deposits) by 1.12 in order to bring it to the end of 1991, then you will get 16502.58
ie.
[12[(1.000236)^730 - 1 / .000236]](1.12) + 15[(1.000311)^365 - 1 / .000311] = 16502.58
a) Tiffany deposits $12 into an account at the end of each day in 1989 and 1990 and $15 at the end of each day in 1991. The account earns an annual effective interest rate of 9% in 1989 and 1990 and an annual effective interest rate of 12% in 1991. Find the amount in Tiffany’s account on December 31, 1991. (Answer: $16,502.58)
b) Rework part (a) using the approximation that the deposits are made continuously. (Answer: $16,504.75)
I think I'm pretty close, just missing something somewhere. I have
12[(1.000236)^730 - 1 / .000236] + 15[(1.000311)^365 - 1 / .000311]
= 15355.5
(because (1+j)^4=1.045 and (1+j)^4=(1.025)^5)
And also I'm not sure for part (b) how you would work it out differently if the deposits are continuous.
Thank you!