I am solving the following problem:
30 y.o. Jack is working a manual job, earning only 8000USD yearly and he isn't expecting any wage increase till his retirement at age 63. However, he is thinking about going to college, which will cost 1000USD yearly. College will take 3 years. After finishing the college, he would > be able to earn 12 000USD yearly until his retirement age. He can't work when studying. Interest rate is 4% p.a.
Is it worth it for Jack to go the college? All financial transactions are realized at the end of each year.
a) (staying in work) $P= 8000*\frac{1-(1+0,04)^{-33}}{0,04}=145181,16$
b) (going to college) = $(-1000)*\frac{1-(1+0,04)^{-3}}{0,04}+12000*\frac{1-(1+0,04)^{-30}}{0,04}*\frac{1}{(1+0,04)^3} = 181 695, 5646$
Is my solution correct?
Thanks