The principle portion of the first payment of a level-payment immediate annuity is given as $\displaystyle prin_{1}=265.21$, and the principle portion of the second payment is given as $\displaystyle prin_{2}=274.49$.

Find n, the number of periods in this annuity.

This is a problem that I just made up. It's based on a problem that I recently encountered, but cannot remember verbatim. In the problem I saw, I believe that the only information given was the principle amount of the first payment and the principle amount of the second payment. The problem then asks to solve for n, the number of periods in the annuity.

How do you go about solving this problem? It doesn't seem as though enough information is given to solve for n.

I can find the interest i by $\displaystyle i=\frac{274.49}{265.21}-1=0.03499$

But without knowing how the value of the payment or the value of the loan, I can't see how to find n.