You rent an apartment that costs \$900$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 to the nearest tenth (if necessary).
To find the rent of the apartment during the 7th year, we need to calculate the amount by which the rent increases each year and then add it to the initial rent.
Step 1: Calculate the amount of rent increase each year.
Rent increase per year = 7.5% of $900
Rent increase per year = (7.5/100) × $900
Rent increase per year = $67.50
Step 2: Calculate the rent during the 7th year.
Rent during the 7th year = Initial rent + (Rent increase per year × Number of years)
Rent during the 7th year = $900 + ($67.50 × 6) (since we are calculating for the 7th year, we multiply the rent increase per year by 6)
Rent during the 7th year = $900 + $405
Rent during the 7th year = $1305
Therefore, the rent of the apartment during the 7th year would be $1305.
To find the rent of the apartment during the 7th year, we need to calculate the rent for each year and then adjust it based on the percentage increase.
First, let's calculate the rent for each year:
Year 1: $900
Year 2: $900 + 7.5% of $900
Year 3: $900 + 7.5% of ($900 + 7.5% of $900)
And so on...
To calculate the rent for each year, we can use the formula:
Rent = Rent(previous year) + (Percentage increase * Rent(previous year))
Using this formula, let's calculate the rent for each year up to the 7th year.
Year 1: $900
Year 2: $900 + 7.5% of $900 = $900 + (0.075 * $900) = $900 + $67.5 = $967.5
Year 3: $967.5 + 7.5% of $967.5 = $967.5 + (0.075 * $967.5) = $967.5 + $72.56 = $1040.06
Year 4: $1040.06 + 7.5% of $1040.06
Year 5: $1040.06 + 7.5% of $1040.06
Year 6: $1040.06 + 7.5% of $1040.06
Year 7: $1040.06 + 7.5% of $1040.06
To find the rent for the 7th year, we repeat the same calculation in Year 7.
Year 7: $1040.06 + 7.5% of $1040.06 = $1040.06 + (0.075 * $1040.06) = $1040.06 + $78.00 = $1118.06
Therefore, the rent of the apartment during the 7th year would be approximately $1118.1.
in year x, the rent will be
900 * 1.075^x