Question

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.)

Answer 1

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

`FV=PV(1+ (r)/(t) )^(nt)`
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).

`FV=100\left(1+ (0.03)/(6) \right)^((48+1))`
Here, we added 1 to the number of period because we are interested in the first month after the fourth year.


`FV=100\left(1+ 0.005 \right)^(49) \\ \\ =100(1.005)^(49) \\ \\ =100(1.276841607)=128` to the nearest whole number.

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