How do you calculate compounding interest problems when you add money over time instead of just invest it all at once? If you invest $50/week in an acct that pays 4% annual interest compounded continuously, how much money do you have in 3 years?

Question

dumbcow · Answer

you have to use a geometric sequence
for continuous interest use e^rt, where r=.04, t = 1/52
$$c = e^{.04/52} = 1.0007695$$
$$B = 50(1+c + c^{2}+...c^{155})$$
$$B = \frac{50(c^{156}-1)}{c-1}$$
$$B = 8,284.11$$