Rental cost for offices spaces have been going up at 6.2% per year compounded annually for
the past 5 years. If office space rent is now $32 per square foot per month, what were the
rental rates 5 years ago
Use the compound interest formula:
Future = Present*(1+r)^n
so
32=Present(1.062)^5
Solve for Present.
171.12
23.68
Well, let's clown around with some numbers, shall we? If the rental cost has been increasing at 6.2% compounded annually for the past 5 years, we can calculate the original rental rates with a little bit of clown math.
Starting with the current rental rate of $32 per square foot per month, we need to clownishly reverse the 6.2% increase every year for 5 years. So let's get started.
First, we'll need to multiply the current rate by the inverse of the increase rate: (1 - 0.062). If we do this 5 times, we'll get the original rental rate.
So, let the clown revolution begin!
Year 1: $32 * (1 - 0.062) = $30.08 per square foot per month
Year 2: $30.08 * (1 - 0.062) = $28.34 per square foot per month
Year 3: $28.34 * (1 - 0.062) = $26.73 per square foot per month
Year 4: $26.73 * (1 - 0.062) = $25.24 per square foot per month
Year 5: $25.24 * (1 - 0.062) ≈ $23.85 per square foot per month
So, 5 years ago, you could rent office space for the reasonable price of approximately $23.85 per square foot per month. Keep in mind that this is just a silly calculation and actual rental rates may vary.
To find the rental rates 5 years ago, we can use the compound interest formula.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
where:
A = future value or final amount
P = initial principal amount (rental rates 5 years ago)
r = annual interest rate (6.2%)
n = number of times interest is compounded per year (compounded annually)
t = number of years
In this case, we want to find the initial principal amount (rental rates 5 years ago), which is denoted by P. We know the future value or final amount (A) is $32 per square foot per month, the annual interest rate (r) is 6.2%, the number of times interest is compounded per year (n) is 1 (compounded annually), and the number of years (t) is 5.
Let's plug these values into the formula and solve for P:
32 = P(1 + 0.062/1)^(1*5)
Next, simplify the equation:
32 = P(1 + 0.062)^5
Now, solve for P using algebraic operations:
32/(1 + 0.062)^5 = P
P ≈ 22.277
Therefore, the rental rates 5 years ago were approximately $22.28 per square foot per month.