what is the net present value of a note for $70,000, PAID MONTHLY AT $600, plus 7% interest
To calculate the net present value (NPV) of a note, you need to discount the future cash flows to their present value and subtract the initial investment. Here's how you can calculate the NPV of the note.
Step 1: Calculate the present value of each monthly payment.
To calculate the present value of each monthly payment, you can use the formula for the present value of an ordinary annuity:
PV = PMT * [1 - (1 + r)^(-n)] / r
Where:
PV = Present value of the cash flow
PMT = Amount of the cash flow per period ($600 in this case)
r = Interest rate per period (7% per period or 0.07)
n = Number of periods (12 months in a year)
Using the formula, we can calculate the present value of each monthly payment:
PV = $600 * [1 - (1 + 0.07)^(-12)] / 0.07
PV ≈ $6,074.83
Step 2: Calculate the NPV.
To calculate the NPV, we subtract the initial investment from the sum of the present values of all cash flows:
NPV = Present value of cash flows - Initial investment
Since the note is worth $70,000, the initial investment is -$70,000 (negative because it's an outflow):
NPV = $6,074.83 - $70,000
NPV ≈ -$63,925.17
The net present value (NPV) of the note is approximately -$63,925.17.