Modelling Quarterly or Monthly Growth Rate to Get a Certain Annual Growth Rate

Let's say I have a quarterly model that starts from a year of actuals that is stagnant (no quarterly growth):
Q1-Y1: 250
Q2-Y1: 250
Q3-Y1: 250
Q4-Y1: 250
Y1 total: 1000

Now if I want the revenue to grow by 10% annually, but with a quarterly model, that's 2.4% quarterly, so for year 2:
Q1-Y2: 256 (Q4 250 x 1.024)
Q2-Y2: 262
Q3-Y2: 269
Q4-Y2: 275
Y2 total: 1062 (so only 6.2% annual growth)

While this makes sense from a quarterly growth concept (if you're flat one year and grow at a rate of 10% annually but on a quarterly basis, you're total annual growth is not gonna be 10%, which makes real world sense), but if the company wants the growth to be 10% on an annual basis but with quarterly growth in this case, I'm having trouble figuring out how to do it.

The only way I can get this to work is if I forecast growth seasonally (so Q over Q of 10% growth rate).

Alternatively, if I start Q1-Y2 at a higher rate, and then go back to my normal 2.4% quarterly growth rate, I could get it to work. But haven't been able to find a formula that does this in a justifiable way.

I'm curious how you guys would tackle a problem like this?