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?

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

andromache andromache · Answer 2 · 2022-03-22T11:36:16+01:00

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

Calculation of the total rent expense:

Here the following formula should be used.

[tex]Sn = (ar^n - 1)\div (r - 1)[/tex]

Here,

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

a means the first term in the sequence.

r means the common ratio.

So,

a = $85000

r = 1 + 6/100 = 1.06

n = 7

Now the total rent should be

= (85000 × 1.06^(7) - 1)/1.06 - 1

= (85000 × 1.06^(7) - 1)/0.06

= 42808.57/0.06

= $713476

hence, The total rent expense be for the entire 7-year lease is $713476

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