Question

You rent an apartment that costs dollar sign, $900 per month during the first year, but the rent is set to go up 7.5% per year. what would be the rent of the apartment during the 7th year of living in the apartment? round your answer to the nearest whole number.

Answer 1

To find the rent of the apartment during the 7th year with an annual increase of 7.5%, you apply the compound interest formula A = P(1 + r)^n. Using $900 as the initial rent and 0.075 as the interest rate, the rent for the 7th year rounds to approximately $1408.

Step-by-step explanation:

To calculate the rent of the apartment during the 7th year of living in the apartment, which increases by 7.5% each year, we will use the formula for compound interest, which is A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (as a decimal), and n is the number of years the money is invested or borrowed for.

In this case, the principal amount P is $900 (the initial rent), the annual interest rate r is 0.075 (since 7.5% as a decimal is 0.075), and the number of years n is 6 (since we are calculating for the 7th year).

The formula for the rent during the 7th year becomes:
A = 900(1 + 0.075)^6

When we calculate this, we get:
A ≈ 900(1.075)^6
A ≈ 900 * 1.564775
A ≈ $1408.30

Rounding to the nearest whole number, the rent during the 7th year would be approximately $1408.