Question

To clear a dead, a person agrees to pay 1000 now, another thousand years from now and another 1000 into years. If the future payments are discounted at 8% compounded quarterly, what is the present value of these payments?

Answer 1

To calculate the present value of the future payments, we need to discount each payment back to the present using the formula for compound interest:

PV = FV / (1 + r)^n

Where:
PV = Present value
FV = Future value
r = Interest rate per compounding period
n = Number of compounding periods

In this case, we are given:
FV1 = 1000 (paid now)
FV2 = 1000 (paid in another thousand years)
FV3 = 1000 (paid into years)
r = 8% compounded quarterly

First, let's calculate the number of compounding periods for each future payment:
Number of compounding periods for FV1 (paid now) = 1 (compounded quarterly)
Number of compounding periods for FV2 (paid in another thousand years) = 1000 * 4 (since it is compounded quarterly)
Number of compounding periods for FV3 (paid into years) = 1000 * 4^2 (since it is compounded quarterly)

Now, let's calculate the present value (PV) for each future payment:
PV1 = FV1 / (1 + r)^n1 = 1000 / (1 + 0.08/4)^1 = $1000
PV2 = FV2 / (1 + r)^n2 = 1000 / (1 + 0.08/4)^(1000 * 4) ≈ $13.38
PV3 = FV3 / (1 + r)^n3 = 1000 / (1 + 0.08/4)^(1000 * 4^2) ≈ $0.18

Finally, let's sum up the present values of all future payments to find the overall present value:
Overall Present Value (PV) = PV1 + PV2 + PV3 ≈ $1000 + $13.38 + $0.18 ≈ $1013.56

Therefore, the present value of these future payments is approximately $1013.56.