# Interest a(t) = a(0)(1 + rt)

1. Jun 17, 2004

### catch.yossarian

In Mathworld, they define Simple Interest as:

a(t) = a(0)(1 + rt)

where a(t) is the sum of principal and interest at time t for a constant interest rate r.

I just want to know why that 0 is in there. Anything divided by 0 will be 0, thus a(t) = 0?

2. Jun 17, 2004

### malco97

I would imagine that a(0) is the principle as it is the sum of the principle and the interest at t=0. Since there is no interest at t=0 the sum of the principle and the interest would be the principle.

3. Jun 17, 2004

Anything divided by 0 is undefined...

They're saying a(t) is a function and a(0) is that function evaluated at t=0.

It would be more clearly written a[t] = (1 + rt)*a[t=0]

4. Jun 17, 2004

### HallsofIvy

In other words, the "a(0)" is not "a times 0", it is "the function a(t) evaluated at t= 0".

5. Jun 17, 2004

### Staff: Mentor

And in still more words (well, actually less words), "a(0)" is the principal.

Ironic - I was just looking for this formula so I could buy a car...

edit: oops - they don't use that formula.

Last edited: Jun 17, 2004
6. Jun 17, 2004

### Gokul43201

Staff Emeritus
Russ,

If you're talking about the depreciation curve, I think that's exponential, not linear.

Edit : No, you're calculating payments, aren't you. I think that's compounded.