My recent marketing idea, the miracle algae growing kit, has been remarkably successful, with monthly sales growing by 3% every 6 months over the past 5 years. assuming that i sold 100 kits the first month, how many kits did i sell in the first month of this year? (round your answer to the nearest whole number.)

The question describes a scenario of an increase of 3% every 6 months copounded monthly with a first term of 100.

To solve this question, we use the future value at compound interest formula noting that here 1 period is 6 months with monthly compounding (i.e. 6 compounding per period).

Recall that the future value at compound interest is given by

where: PV is the sale made in the first month = $100, r is the increase per period = 3%, t is the number of compounding every month = 6, n is the number of periods = 8 x 6 = 48 (8 periods of 6 months each).

Here, we added 1 to the number of period because we are interested in the first month after the fourth year.

to the nearest whole number.

Therefore, 128 kits was sold in the first month of this year.