# Calculating average interest rate with intermittent deposits

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)

If I understand your question correctly I think the easiest solution would be to use the XIRR formula in Excel. You can have a column of dates, and a column of cash flows, and it will calculate the rate for you.

Description

Returns the internal rate of return for a schedule of cash flows that is not necessarily periodic. To calculate the internal rate of return for a series of periodic cash flows, use the IRR function.