If I want my rent in 4yrs to be 900dllrs. The owner of the apartment building told me that the rent will increase 3% every year compounded every year. What should be my rent today?
The formula for compound interest (which this problem asks about) is:
A = P(1+(r/n))^(nt)
Where A is the amount you end with, P is the original/beginning amount, r is the interest rate, n is the number of times interest is compounded, and t is the number of years. So because n = 1, this is what you'll be working with:
A = P(1+r)^t
You'll be solving for P because you want to know what rent should be at the beginning of the lease. So the formula should be rearranged as follows:
P = A/((1+r)^t)
All I did was solve the formula for P.
Now A = $900, r = 0.03, and t = 4.
Plug and solve and you'll have your answer.
710.78 to the nearest cent: 710.79 either one will be correct.
To calculate your rent today, we need to use the formula for compound interest. The formula is:
P = A / (1 + r)^n
Where:
P = present value (rent today)
A = future value (rent in 4 years)
r = interest rate (3% or 0.03)
n = number of compounding periods (in this case, 4 years)
First, let's calculate the future value (A):
A = $900 (desired rent in 4 years)
Next, let's substitute the known values into the formula and solve for P:
P = $900 / (1 + 0.03)^4
P = $900 / (1.03)^4
Now, calculate the value in the parentheses:
(1.03)^4 = 1.1255
Now, divide the future value by the result:
P = $900 / 1.1255
P ≈ $800.71
Therefore, your rent today should be approximately $800.71.