Jack Brown received two offers for his property: 1. 130000 in 5 months. 2. $13500 every months for the next 10 months. Find the present value of the two offers if theory is worth 12% compounded monthly.
To find the present value of the two offers, we need to calculate the present value (PV) of each offer and then compare them.
Let's start with the first offer:
Offer 1: $130,000 in 5 months
To calculate the present value of this offer, we need to use the formula for the present value of a single amount:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Interest rate (expressed as a decimal)
n = Number of periods
In this case, the future value (FV) is $130,000, the interest rate (r) is 12% (or 0.12 as a decimal), and the number of periods (n) is 5 months.
Substituting these values into the formula, we get:
PV = $130,000 / (1 + 0.12/12)^5
Simplifying this expression:
PV = $130,000 / (1 + 0.01)^5
PV = $130,000 / (1.01)^5
PV ≈ $109,355.31
So the present value of the first offer is approximately $109,355.31.
Now let's move on to the second offer:
Offer 2: $13,500 every month for the next 10 months
This offer consists of a series of equal cash flows. To calculate the present value of this offer, we will use the formula for the present value of an ordinary annuity:
PV = CF × [1 - (1 + r)^(-n)] / r
Where:
PV = Present Value
CF = Cash Flow per period
r = Interest rate (expressed as a decimal)
n = Number of periods
In this case, the cash flow (CF) is $13,500, the interest rate (r) is 12% (or 0.12 as a decimal), and the number of periods (n) is 10 months.
Substituting these values into the formula, we get:
PV = $13,500 × [1 - (1 + 0.12/12)^(-10)] / (0.12/12)
Simplifying this expression:
PV = $13,500 × [1 - (1.01)^(-10)] / (0.01)
PV ≈ $117,355.92
So the present value of the second offer is approximately $117,355.92.
Therefore, the present value of the first offer is $109,355.31 and the present value of the second offer is $117,355.92.