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?
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.
To find the present value of future payments, we need to discount each payment back to its present value.
Given:
Payment 1: $1000 due now
Payment 2: $1000 due in another thousand years
Payment 3: $1000 due in another thousand years
Discount rate: 8% compounded quarterly
Step 1: Calculate the present value of each payment separately.
1. Payment 1: $1000 due now
Since this payment is due now, its present value is equal to its face value.
Present value of Payment 1 = $1000
2. Payment 2: $1000 due in another thousand years
To calculate the present value of Payment 2, we need to discount it back to its present value.
The number of quarters in a thousand years = 1000 * 4 = 4000 quarters
Discount rate per quarter = 8% / 4 = 2% per quarter
Using the present value formula for quarterly compounding:
Present value of Payment 2 = $1000 / (1 + 0.02)^4000
3. Payment 3: $1000 due in another thousand years
To calculate the present value of Payment 3, we use the same formula as Payment 2:
Present value of Payment 3 = $1000 / (1 + 0.02)^4000
Step 2: Calculate the total present value of all three payments.
Total present value = Present value of Payment 1 + Present value of Payment 2 + Present value of Payment 3
Note: The present values of Payments 2 and 3 need to be calculated using a calculator.
After performing the calculations, you will obtain the present value of the future payments.
To calculate the present value of future payments, we need to discount each payment back to the present using the given interest rate. Let's break down the problem step by step.
First, let's calculate the present value of each payment separately.
1) The first payment of $1000 is due now, so its present value is simply $1000.
2) The second payment of $1000 is due in one thousand years. To discount it to the present, we need to find the present value of $1000 in one thousand years. We can use the compound interest formula to calculate it:
PV = Future Value / (1 + (r/n))^(n*t)
Where:
PV = Present Value (what we want to find)
Future Value = $1000 (the payment in one thousand years)
r = Interest rate per year (8% or 0.08)
n = Number of compounding periods per year (quarterly, so 4)
t = Number of years (one thousand years)
Using these values, we can plug them into the formula:
PV = $1000 / (1 + (0.08/4))^(4 * 1000)
Calculating this gives us the present value of the second payment.
3) The third payment of $1000 is due in two thousand years. Using the same compound interest formula as above, we can calculate its present value:
PV = $1000 / (1 + (0.08/4))^(4 * 2000)
Calculate this to find the present value of the third payment.
Finally, to find the total present value, we add up the individual present values:
Total Present Value = Present Value of the first payment + Present Value of the second payment + Present Value of the third payment
Calculate this sum to find the present value of the three payments.
Note: The compound interest formula assumes that the interest is compounded at regular intervals (quarterly in this case). If the compounding is not mentioned or specified, it's a good idea to clarify it before calculating the present value.