Question

You rent an apartment that costs $1200 per month during the first year, but the rent is set to go up 11% per year. What would be the rent of the apartment during the 8th year of living in the apartment? Round your answer to the nearest whole number.(1 point)
a8 =
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Answer 1

To calculate the rent during the 8th year, we start with the first year's rent and apply the annual increase of 11% for each subsequent year.

1. The first year’s rent is \( R_1 = 1200 \).
2. For each year \( n \), the rent can be calculated using the formula for compound interest:

\[
R_n = R_1 \times (1 + r)^{(n-1)}
\]

where:
- \( R_n \) is the rent in year \( n \),
- \( R_1 \) is the initial rent,
- \( r \) is the rate of increase (in decimal form), and
- \( n \) is the year number.

In this case:
- \( R_1 = 1200 \)
- \( r = 0.11 \)
- We want to find \( R_8 \).

Now plug the values into the formula to calculate \( R_8 \):

\[
R_8 = 1200 \times (1 + 0.11)^{(8-1)} = 1200 \times (1.11)^7
\]

Now let's calculate \( (1.11)^7 \):

\[
(1.11)^7 \approx 2.5023
\]

Now we multiply this result by the initial rent:

\[
R_8 \approx 1200 \times 2.5023 \approx 3002.76
\]

Rounding this to the nearest whole number gives us:

\[
R_8 \approx 3003
\]

Thus, the rent during the 8th year of living in the apartment is approximately:

\[
\boxed{3003}
\]