A house is rented for $2000 per quarter, with each quarter's rent payable in advance. If money is worth 2%, compounded quarterly, and the rent is deposited in an account, what is the future value of the rent for one year?
Assume 2% is per quarter (not per annum).
so R=1.02, n=4 quarters, and rent, P=$2000.
Future value
P(R+R^2+R^3+R^4)
= PR(1+R+R^2+R^3)
=PR (R^4-1)/(R-1)
=2000*1.02*(1.02^4-1)/(1.02-1)
=$8408.08
Well, it looks like we're dealing with some math here. But don't worry, I'm here to put a silly spin on it!
So, let's break it down. Each quarter, you're paying $2000 in advance, right? And since we're talking about future value, we need to take into account the interest rate and compounding.
Now, let's do some calculations. To find the future value of the rent for one year, we're looking at four quarters. So we start with $2000 and compound it for each quarter.
After the first quarter, you'll have $2000 x (1 + 2%/4) = $2000 x 1.005 = $2010.
After the second quarter, you'll have $2010 x (1 + 2%/4) = $2010 x 1.005 = $2015.02.
After the third quarter, you'll have $2015.02 x (1 + 2%/4) = $2015.02 x 1.005 = $2020.07.
And finally, after the fourth quarter, you'll have $2020.07 x (1 + 2%/4) = $2020.07 x 1.005 = $2025.12.
So, the future value of your rent for one year is approximately $2025.12.
I hope that brings a smile to your face, even if calculating future value isn't the most exciting thing in the world!
To find the future value of the rent for one year, we need to calculate the future value of each individual quarterly payment and then sum them up.
Given information:
Rent per quarter = $2000
Interest rate (compounded quarterly) = 2%
Number of quarters in one year = 4
Step 1: Calculate the future value of one quarterly payment.
Using the formula for the future value of a single payment, we have:
FV = PV * (1 + r)^n
Where:
PV = Present value (rent per quarter) = $2000
r = Interest rate per period = 2% = 0.02 (converted to decimal)
n = Number of periods = 1 (since we're calculating the future value for one payment)
FV = $2000 * (1 + 0.02)^1
FV = $2000 * (1.02)^1
FV = $2000 * 1.02
FV = $2040
So, the future value of one quarterly payment is $2040.
Step 2: Calculate the future value of all four quarterly payments for one year.
Since the rent is payable in advance for each quarter, we are effectively depositing the rent at the beginning of each quarter.
So, we need to calculate the future value of each individual quarterly payment and sum them up for one year.
FV_total = FV_payment1 + FV_payment2 + FV_payment3 + FV_payment4
FV_total = $2040 + $2040 + $2040 + $2040
FV_total = $8160
Therefore, the future value of the rent for one year is $8160.
To find the future value of the rent for one year, we need to calculate the value of each quarter's rent after one year and then add them together.
First, let's determine the value of each quarter's rent after one year. Since the rent is paid in advance, we treat it as a series of lump sum payments deposited at the beginning of each quarter.
Given that the rent is $2000 per quarter, we need to find the future value of $2000 over one year, considering a 2% interest rate compounded quarterly.
To calculate the future value, we can use the formula for compound interest:
Future Value = Present Value * (1 + interest rate / number of periods)^(number of periods)
In this case, the interest rate is 2% and compounded quarterly, so we have:
Present Value = $2000
Interest Rate = 2% = 0.02
Number of Periods = 1 year * 4 quarters = 4
Now we can substitute the values into the formula:
Future Value = $2000 * (1 + 0.02 / 4)^(4)
Calculating this expression gives:
Future Value = $2000 * (1.005)^(4)
Future Value = $2000 * 1.020201
Future Value = $2040.40 (rounded to two decimal places)
So, the future value of each quarter's rent after one year is approximately $2040.40.
Since there are four quarters in one year, we can multiply the future value of each quarter's rent by four:
Total Future Value = $2040.40 * 4
Total Future Value = $8161.60
Therefore, the future value of the rent for one year, when deposited into an account with a 2% interest rate compounded quarterly, is approximately $8161.60.