Determining a non-linear non-constant rate of growth [University - Finance]

I cannot estimate the growth rate, especially if non not held constant through time, without knowing the premiums retained per year.

You can see that on year one, despite having paid $288.48, you can only cash out $100.23, suggesting $188.25 was expensed as a premium. A constant premium of $188.25, assuming a constant interest rate as well, cannot match these numbers.

I'm trying to guess the model here, since you're not providing much information, but my first guess would be something akin to :

Sum(n = 1 to 40) (288.48 - P(n))(1+r(n))n-1,

where P(n) is the premium on the nth year and r(n) is the return rate between the nth and (n+1)st year. There is no constant real r and P such that r(n) = r and P(n) = P for all n that make the series respect the model. So either the premium or the interest rate is not constant (say if they are hedging their funds using forward rates) and/or the premium (if the premium follows an implicit dynamic).

Or it's an different model. Really hard to guess just looking at this series without more information.

/r/learnmath Thread