How to find the Rate of Interest when we know the Principal Outstanding, Monthly Annuity Amount but do not know the number of annuities remaining.

Question

I frequently face situations where I have to calculate the Rate of Interest/Interest Amount on a loan.

The following is the data I have in hand:

1. Principal Outstanding: 772,456
2. Monthly Annuity. : 47,214

I do not know the following:

1. Number of annuities remaining.
2. Rate of Interest
3. Initial Loan Period

There are two missing variables here and only one equation to help us solve. Seems impossible to solve. But I gave it a thought and realised that the rate of Interest will be in a range of 8% p.a to 16% p.a. and also the Rate of Interest will be restricted to 1 place after decimal (Allowed : 13.10 %, Not Allowed: 13.11 %). With this data can we find out the Rate of Interest, if not exactly but at least a close approximate?

I want to develop a model to solve such problems every time I face them.

Thanks!