A 7-year lease for office space states that the annual rent is $85,000 for the first year and will increase by 6% each additional year of the lease. What will the total rent expense be for the entire 7-year lease?

Question

Mathematics

Daniella Drake

23 September, 13:54

A 7-year lease for office space states that the annual rent is $85,000 for the first year and will increase by 6% each additional year of the lease. What will the total rent expense be for the entire 7-year lease?

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Answers (1)

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Dracula · Answer 1

Answer: the total rent expense be for the entire 7-year lease is $713476

Step-by-step explanation:

The rate at which the rent increases each year is in geometric progression. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1) / (r - 1)

Where

n represents the number of term (years) in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

a = $85000

r = 1 + 6/100 = 1.06

n = 7

Therefore, the sum of the first 7 terms (7 year lease), S7 is

S7 = (85000 * 1.06^ (7) - 1) / 1.06 - 1

S7 = (85000 * 1.06^ (7) - 1) / 0.06

S7 = 42808.57/0.06

S7 = $713476