Help me calculate interest...

[_TKO_]

...for a Savings account.

Assuming I don't remove funds ever, how do I calculate my earnings over m months if interest is calculated on my daily balance, but paid once every month?

Please list any other assumptions you are making.

[garion888]

I = P*(1+r)^n

n = number of time periods
r = rate per time period
P = Principal
I = Interest

Calculate to your hearts content...

[ScottieK]

Motley Fool calculators page

Knock yourself out.

ScottieK

[_TKO_]

I don't think either of you were able to answer my question.

[Borodog]

Your problem is complicated by the fact that different months have different numbers of days. I'm goint to assume all 30 day months, and hence a 360 day year.

The annual percentage interest rate is defined to be i.

The balance at month m is defined to be B(m).

The principle is the balance prior to the first month, or B(0).

The balance each month depends on the previous month's balance, compounded at the daily interest rate (i/360) for 30 days:

B(m) = B(m-1)[1+i/360]^30

B(m) = B(0)[1+i/360]^(30m)

But your earnings do not include the original deposit, so:

Earnings = B(0)[[1+i/360]^(30m)-1]

[Borodog]

A more accurate answer would calculate the real daily interest rate i/365, and use the actual number of days for each month.