It costs $850 per month to rent an apartment. The monthly cost increases by 3% each year. Find the monthly cost in 10 years.
Understand the Problem
The question is asking us to calculate the future monthly cost of renting an apartment under a 3% annual increase over 10 years, starting from a base cost of $850 per month.
Answer
The future monthly cost will be approximately $1153.91.
Answer for screen readers
The monthly cost in 10 years will be approximately $1153.91.
Steps to Solve
- Understand the formula for compound interest
We can use the formula for compound interest to solve for the future cost:
$$ A = P(1 + r)^t $$
where:
- ( A ) = the amount of money accumulated after n years, including interest.
- ( P ) = the principal amount (the initial amount).
- ( r ) = the annual interest rate (decimal).
- ( t ) = the number of years the money is invested or borrowed.
- Identify the variables
In our case:
- The initial monthly rent ( P = 850 )
- The annual increase rate ( r = 0.03 ) (3%)
- The number of years ( t = 10 )
- Plug in the values
Substituting the identified values into the compound interest formula:
$$ A = 850(1 + 0.03)^{10} $$
- Calculate the future value
First, calculate ( 1 + 0.03 = 1.03 ).
Then, compute ( (1.03)^{10} ).
- Final multiplication
Finally, multiply the result by 850 to get the future monthly cost.
The monthly cost in 10 years will be approximately $1153.91.
More Information
This calculation is based on a continuous increase where the rent increases 3% each year for a decade. This method applies to various financial scenarios, such as savings and investments.
Tips
- Not converting the percentage into a decimal form; remember that 3% must be written as 0.03.
- Forgetting to use parentheses in calculations leading to incorrect order of operations.
- Miscalculating the exponentiation; this can lead to significant errors in the final amount.
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