Question

You rent an apartment that costs dollar sign, 1600$1600 per month during the first year, but the rent is set to go up 10% 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.

Answer 1

To determine the rent in the 8th year after a 10% annual increase from an original rent of $1600, use the compound interest formula with 7 years of increase, resulting in a rent for the 8th year of approximately $3118.

Step-by-step explanation:

The question asks how much the rent will be in the 8th year if it starts at $1600 and increases by 10% per year. The calculation involves finding the future value of the rent after 7 years of increase (since the first year is at the initial rent rate, and we are looking for the rent at the start of the 8th year).

We can do this using the formula for compound interest:

Future Value = Present Value * (1 + rate)^n

Where:

• Present Value (PV) is the initial rent amount, which is $1600.
• rate is the yearly increase rate, which is 10% or 0.10.
• n is the number of years, which is 7.

So the calculation will be:

Future Value = 1600 * (1 + 0.10)^7

Doing the calculation:

Future Value = 1600 * (1.10)^7

Future Value = 1600 * 1.9487171

Future Value ≈ 3117.95

Rounding this to the nearest whole number, the rent during the 8th year would be approximately $3118.