How do you work out compound interest with irregular contributions compounded quarterly?

Answer 1

By definition, quarterly compounding means the interest is calculated at the end of each quarter on the balance at that time, including all contributions paid during that quarter.

Let B be the balance at the beginning of a quarter and S be the sum of all the payments (can be more than one payment) during that quarter.

Let i be the annual interest. The quarterly interest is then i/4.

The new balance for the beginning of the next quarter is then,
New balance = B*i/4 + S*i/4 = (B+S) * i/4 .

You do this calculation at the end of each quarter. Of course at the beginning of next quarter, the new balance becomes the beginning balance B and from the total contributions of that quarter you calculate the new balance for that quarter. The quarterly interest stays the same.

Answer 2

With a fractional annual interest rate r compounded quarterly, the amount A at time t years after an individual contribution P is made is:
A = P(1 + r/4)^(4t)
This is the amount only from that individual contribution.
As the contributions are irregular, you would have to perform this calculation for each of the contibutions separately and then add up all the values of A. If the interest rate r changes the formula is even more complex.

Answer 3

Your period is the quarter and your quarter interest rate is i_q = (i_m - 1)^(1/4), where i_m is the montly interest rate.

Answer 4

Please read a book on consumer mathematics particularly on topics about "ANNUITY". Your problem can be best solved through the concept of annuity. And it takes days to fully understand about annuity.