you rent an apartment that costs $1600 per mo...
you rent an apartment that costs $1600 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 10th year of living in the apartment? round your answer to the nearest whole number.
Answer
# Explanation:
## Step1: Identify the formula
The formula for compound - growth is $A = P(1 + r)^{n}$, where $P$ is the initial amount, $r$ is the rate of growth as a decimal, and $n$ is the number of years. Here, $P = 1600$, $r=0.125$, and $n = 9$ (since we are finding the rent in the 10th year, so the number of growth - periods is 9).
## Step2: Substitute the values
$A=1600\times(1 + 0.125)^{9}$.
First, calculate $(1 + 0.125)=1.125$. Then, find $1.125^{9}$.
$1.125^{9}\approx2.755625$.
## Step3: Calculate the final amount
$A = 1600\times2.755625=4408.9999\approx4409$.
# Answer:
$4409$