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You rent an apartment that costs
$900 per month during the first year, but the rent is set to go up
12.5% per year. What would be the rent of the apartment during the 6th year of living in the apartment? Round your answer to the nearest whole number.
Answer:
$ □

You rent an apartment that costs $\$ 900$ per month during the first year, but the rent is set to go up $12.5 \%$ per year. What would be the rent of the apartment during the $6$ th year of living in the apartment? Round your answer to the nearest whole number. $\newline$ Answer: $\$$ $\square$

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Exponential growth and decay: word problems

Full solution

Q. You rent an apartment that costs

\$ 900

per month during the first year, but the rent is set to go up

12.5 \%

per year. What would be the rent of the apartment during the

6

th year of living in the apartment? Round your answer to the nearest whole number.

\newline

Answer:

\$

\square

Identify Rent Details: Identify the initial rent and the annual percentage increase. $\newline$ The initial rent is $\$900$ per month, and the rent increases by $12.5\%$ each year.
Convert Percentage to Decimal: Convert the percentage increase to a decimal to use in calculations. $12.5\%$ as a decimal is $0.125$ .
Formula for Rent Calculation: Determine the formula to calculate the rent after a certain number of years. $\newline$ The rent after $n$ years can be calculated using the formula: $\text{Rent}_n = \text{Rent}_0 \times (1 + \text{rate})^n$ , where $\text{Rent}_0$ is the initial rent, $\text{rate}$ is the annual increase rate, and $n$ is the number of years.
Calculate Rent for $6$ th Year: Calculate the rent for the $6$ th year using the formula. $Rent_6 = \$900 \times (1 + 0.125)^5$ , since the rent is calculated at the beginning of the $6^{th}$ year, we use $n = 5$ .
Perform Calculation: Perform the calculation. $\newline$ $Rent_6 = \$900 \times (1.125)^5$ $\newline$ $Rent_6 = \$900 \times 1.769$ $\newline$ $Rent_6 = \$1592.10$
Round to Nearest Whole Number: Round the answer to the nearest whole number. $\newline$ The rent during the $6^{\text{th}}$ year, rounded to the nearest whole number, is $\$1592$ .

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