Financial formula for calculating an Adjustable Rate Mortgage?

Question

How can I calculate a fixed payment amount for a loan term that has two different interest rates based on how long the loan has been open?

Accepted Answer

This gets a little ugly, so please bear with me.

Define:

- g1 = Initial monthly rate (For 3%, g=0.03/12.)

- g2 = Second monthly rate.

- T1 = Term for the initial rate (T1 = 3 for 3 months).

- T2 = Term for the subsequent rate.

- u1 = 1 / (1 + g1)

- u2 = 1 / (1 + g2)

Then:

- payment = g1 * g2 / (g1 * u1^T1 * (1 - u2^T2) + g2 * (1 - u1^T1))

Of course, I may have made a mistake, but that seems right.

Solution