Log-linear trend model

What is the annual growth rate for the stock index according to the log-linear trend model?

He prepares a log-linear trend model for the movement of the stock index. The value of the time series dependent variable at time t is given by ln(yt) = 7.8 + 0.098*t; where the frequency period for time t is annual. The yt represents the value of the index level at time t.

t = 1, e(.098*1+7.8), find the other ones to find growth rate

The solution says (e.098)-1=10.3% Is this correct?

So basically it’s asking you to find the growth rate from t = 0 to t = 1

You find the value at t=0. e7.8

Then, you find the value of t=1, e(.098+7.8)

Now you can find the growth rate, 2691.89/2440.60 -1 = .102963

This way is just slower, easier to understand, but the mathematical logic is the same

Got it. Thanks!