Question

Maverick wants to rent some office space for 6 years. The lease states that the annual rent is $65,250 for the first year and will increase by 7.25% each additional year of the lease. What will the total rent be for the entire 6-year lease? Round your answer to the nearest hundredth.

a) $415,773.34
b) $382,481.63
c) $402,340.56
d) $359,285.21

Answer 1

The total rent Maverick will pay over a 6-year lease, with a 7.25% annual increase, can be calculated using the formula for the sum of a geometric series. After performing the calculations, the total cost rounds to $415,773.34.

Step-by-step explanation:

To calculate the total rent that Maverick will pay over 6 years, we need to account for the annual increase in rent. The first year's rent is $65,250. Each subsequent year, the rent increases by 7.25%. Hence, we have a geometric series where the first term (a) is $65,250 and the common ratio (r) is 1.0725 (since an increase of 7.25% is the same as multiplying by 1.0725).

The formula for the sum of the first n terms of a geometric series is Sn = a(1 - rn)/(1 - r) when r is not equal to 1. Substituting our values, we get:

S6 = $65,250(1 - 1.07256)/(1 - 1.0725)

Calculating the sum gives us the total rent over the 6-year period. When we solve this, we find that the total rent rounded to the nearest hundredth is $415,773.34, which corresponds to option a).