Question

you rent an apartment that costs $1600 per month during the first year ,but the rent is set to go up 11.5% per year.what would be rent of the apartment during the 10th year of living in the apartment? round to the nearest tenth (if necessary ).​

Answer 1

The rent of the apartment during the 10th year would be approximately $4,565, after accounting for an 11.5% annual increase from the original rent of $1,600 per month.

Step-by-step explanation:

To calculate the rent of the apartment during the 10th year, we need to account for the 11.5% annual increase. The formula to calculate the future value of the rent after a certain number of years with a consistent percentage increase is:

R = P(1 + r)^n

Where:

• R is the rent after n years,
• P is the initial rent ($1,600),
• r is the annual increase rate (11.5% or 0.115), and
• n is the number of years (10).

By applying this formula:

R = 1600(1 + 0.115)^10

Let's calculate:

1. First, add 1 to the increase rate: 1 + 0.115 = 1.115.
2. Next, raise this sum to the power of 10: (1.115)^10.
3. Then, multiply the result by the initial rent to find the rent after 10 years.

When you perform these calculations, this gives:

R ≈ 1600 * 2.8531

R ≈ $4564.96

Therefore, rounded to the nearest tenth, the rent during the 10th year would be about $4,565.