Find the cost of the monthly rent for a two-bedroom apartment in 30 years, assuming an inflation rate of 5% (compounded continuously), if the current rent is $610. (Round your answer to the nearest cent.)
What is 610(e^(30(.05)) ) ?
What do you mean by e
e is Euler's number, it is appr 2.718281828...
It is also the base of the natural logarithm or "ln" on your calculator.
You will need it if you are solving problem where the interest rate is compounded continuously. I am surprised you have not come across this
number, since clearly you are dealing with this type of question
I got confused for a second. You are a life saver!
2733.83
To find the cost of the monthly rent for a two-bedroom apartment in 30 years, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A is the final amount
P is the initial amount
e is the base of the natural logarithm (approximately 2.71828)
r is the interest rate
t is the time in years
In this case, the initial amount (P) is $610, the interest rate (r) is 5% (0.05 in decimal form), and the time (t) is 30 years.
Plugging in these values into the formula, we get:
A = 610 * e^(0.05 * 30)
Now, let's calculate it step by step:
Step 1: Calculate the exponential term
e^(0.05 * 30) ≈ 2.71828^(0.05 * 30) ≈ 2.71828^1.5 ≈ 4.481689
Step 2: Multiply the initial amount by the exponential term
610 * 4.481689 ≈ 2736.41
Therefore, the cost of the monthly rent for a two-bedroom apartment in 30 years, assuming an inflation rate of 5% (compounded continuously), is approximately $2736.41.