If $12,000 is invested in a certain business at the start of the year, the investor will receive $3,600 at the end of the next four years. What is the present value of this business opportunity if the interest rate is 7% per year?

Fiona Plans To Invest $500 Later Today. She Wants To Know To What Amount Her Investment Will Grow In 20 Years If She Earns 12 Percent Interest Compounded (a0 Annually, (b) Quarterly, And (c) Monthly

4823.15

To find the present value of the business opportunity, we can use the formula for the present value of a future cash flow:

PV = FV / (1+r)^n

Where:
PV = Present Value
FV = Future Value
r = Interest Rate
n = Number of years

In this case, the future value (FV) is $3,600, the interest rate (r) is 7% or 0.07, and the number of years (n) is 4.

Substituting these values into the formula, we get:

PV = $3,600 / (1+0.07)^4

Calculating the denominator: (1+0.07)^4 = 1.310796

PV = $3,600 / 1.310796

Using a calculator, we find:

PV ≈ $2,747.25

Therefore, the present value of this business opportunity is approximately $2,747.25.

To find the present value of this business opportunity, we need to discount the future value of $3,600 back to the present using the given interest rate of 7% per year.

The formula to calculate the present value (PV) of a future value (FV) is:
PV = FV / (1 + r)^n

Where:
PV = Present value
FV = Future value
r = Interest rate
n = Number of time periods

In this case, FV is $3,600, the interest rate (r) is 7% (or 0.07 as a decimal), and the time period (n) is 4 years.

Let's plug in the values into the formula:
PV = $3,600 / (1 + 0.07)^4

First, we calculate 1 + 0.07 = 1.07.
Next, we raise 1.07 to the power of 4: 1.07^4 = 1.3108 (rounded to four decimal places).
Finally, we divide $3,600 by 1.3108 to find the present value:
PV = $2,746.08 (rounded to two decimal places).

Therefore, the present value of this business opportunity is approximately $2,746.08 if the interest rate is 7% per year.