Compound Interest: 3.11% Annually, 3x/Year

[pbuk]

That is all fine, but when I wrote that I was referring to this

Oh I see

Reading that back I could have phrased it better:

Interest is normally calculated on a daily basis (using some conventional calculation - see below) increasing the value of the investment (almost) continuously. However this does not mean that the interest compounds continuously, the calculated amount is added to a separate balance ("accrued interest") from the sum that is used to calculate interest (the "principal"). At each relevant date the balance of accrued interest is transferred to the principal ("rolled up") or paid to the investor.

The daily interest calculation is set by the contract and/or conventions of the particular financial instrument and will follow one of a number of surprisingly arcane procedures some of which are outlined here.

 

[Chestermiller]

Oh I see

Reading that back I could have phrased it better:

Interest is normally calculated on a daily basis (using some conventional calculation - see below) increasing the value of the investment (almost) continuously. However this does not mean that the interest compounds continuously, the calculated amount is added to a separate balance ("accrued interest") from the sum that is used to calculate interest (the "principal"). At each relevant date the balance of accrued interest is transferred to the principal ("rolled up") or paid to the investor.

The daily interest calculation is set by the contract and/or conventions of the particular financial instrument and will follow one of a number of surprisingly arcane procedures some of which are outlined here.

In line with this and what @etotheipi said in post #11, A(t) should really be a discontinuous function of t, with the discontinuities occurring on every compounding date (or whatever it's called), and A(t) should more properly be expressed with the nt in the exponent being replaced by $$\sum_{m=1}^{\infty}u\left(t-\frac{m}{n}\right)$$where u(x) is the unit step function, equal to 0 if its argument is less than zero and 1 if its argument is greater than zero. So, more properly, A(t) should read $$A(t) = I\left(1+\frac{r}{n}\right)^{\sum_{m=1}^{\infty}u\left(t-\frac{m}{n}\right)}$$