I invest in a few medium to low risk accounts online (peer to peer loans and buy to let property crowdfunding).
I make regular deposits into these accounts, usually when the monthly salary comes in, but the time period between my deposits and the amount changes.
I know how to work out the effective APR from interest earned on a single deposit over a time span, for example, taking C (capital deposit), P (profit from interest), and T (time span in days) it would be:
APR = ((P/C + 1)^(365 / T) - 1) * 100
But if I then extend this to be over two time periods, taking: C1 and C2 (starting amounts), T1 and T2 (timespans in days), P (total interest earned), and I (daily interest rate for simplicity)
P = (C1 * (I^T1 - 1)) + (C2 * (I^T2 - 1))
Is there a direct method to get the average interest rate (I) over the two periods, knowing all other variables?
I have attempted to create an iterative formula by rearranging to get one of the I's on one side:
I = (((P - C2 * (I^T2 - 1)) / C1) + 1) ^ (1/T1)
Taking the initial value of I as 1. But this equation diverges when I try to iterate it.
Is there either an iterative approach which converges or a direct approach?
(Money stack exchange does not have MathJax so I will repost these formulae as images once I have enough rep)