You rent an apartment that costs $1200 per month during the first year, but the rent is set to go up 10.5% per year. What would be the rent of the apartment during the 7th year of living in the apartment?

The rent of the apartment during the 7th year of living in the apartment is $2,414 per month (or $28,968 for the whole full year)

Step-by-step explanation:

Here, we are to estimate the cost of an apartment in the 7th year of living in the apartment, given the cost per month in the first year.

Now, since the cost per month in the first year is $1200, the cost per year will be 1200 * 12 = $14,400

Now to calculate the cost at the 7th year, we shall need to model and exponential equation. This is;

C = I (1+r) ^t

where C is the cost per year

I is the cost in the first year which is $14,400

r is the increment percentage = 10.5% or simply 10.5/100 = 0.105

and t is the year in question which is 7

Plugging these values we have;

C = 14,400 (1 + 0.105) ^7

C = 14,400 (1.105) ^7

C = 28,966.66 which is approximately $28,967

Thus the cost per month in the 7th year will be 28,967/12 = 2,413.9 which is approximately $2,414