I'm trying to solve a finance question, and am getting slightly confused. The question is as follows:
On Jan. 1st, 2000, 3500 dollars is deposited into a bank account. On Jan. 1st 2005, 4000 dollars is deposited. On Jan. 1st 2009, 2500 dollars is deposited. Assuming that there are no withdrawals/deposits, what is the effective interest rate if the account contains $13,035.10 on Jan. 1st 2014?
Now, I know this is probably not a difficult question. But I'm having trouble understanding the laws. So I think we should break it up into groups, the first being 3500 dollars for 5 years, the next being 7500 dollars for 4 years, and then 10,000 dollars for 5 years. All of which combine to give the final value. However, I'm not sure how to break this up properly and still have an equation in which we can find the value of 'i'. Any help would be appreciated !
Assuming that interest is compounded annually at a rate of $r$, then we have
$$3500(1+r)^{14}+4000(1+r)^{9}+2500(1+r)^5=13035.1$$
Solving numerically, we find that
$$r\approx 2.71000160179451\text{%}$$