Finance Question (involving interest that is added)

Question

I have 2 questions involving this concept, that I am looking for an answer for.

1. Tony is considering putting 50 dollars per month into a special account that would earn 6.25% annual interest. How much would Tony have in his account after 25 years? (nearest cent) (Answer is 36,013.70) I am looking for a formula that would get me this answer

2. Ross puts 250 dollars into her retirement account at the end of each quarter of the year. The account pays interest of 4 percent compounded quarterly. How much will be in Ross's account at the end of the 1st year? (Answer is 1,015.10) I am looking for a formula that would get me this answer as well

I've tried using this formula Balance(Y) = P(1 + r)Y + c[ ((1 + r)Y - 1) / r ] but it doesn't give exact answers I'm looking for.

Answer 1

Hints:

1. Let´s say you have an annual interest rate $i$ and you put $x$ dollars per month on an account every month. Then the amount of money on Tony´s account after $n$ months is

$$C_n=x\cdot \frac{(1+\frac{i}{12})^n-1}{\frac{i}{12}}$$

2. Here the formula is similar. After $n$ quarters the amount of money on Ross' account is $$C_n=x\cdot \frac{(1+\frac{i}{4})^n-1}{\frac{i}{4}}$$

Do you see the pattern?