To clear a debt, a person agrees to pay thousand now, another 1000 a year from now and another thousand in 2 years. If the future payments are discount at 8% compounded quarterly, what is the present value of these payments?

Answer 1

To find the present value of the future payments, we need to discount each payment back to its present value using the given interest rate.

Let's calculate the present value for each payment separately.

First payment of $1000:
Since this payment is made now, its present value is equal to its future value. So, the present value of the first payment is $1000.

Second payment of $1000 [after 1 year]:
To find the present value of this payment, we need to discount it back 1 year at an interest rate of 8% compounded quarterly. Quarterly compounding means that the interest rate per quarter is 8%/4 = 2%.

Using the compound interest formula, the present value (PV) of the second payment can be calculated as:
PV = FV / (1+r)^n
Where FV is the future value, r is the interest rate per period, and n is the number of periods.

In this case, FV = $1000, r = 2% or 0.02, and n = 4 (since there are 4 quarters in a year).
PV = $1000 / (1+0.02)^4
PV = $1000 / (1.02)^4
PV ≈ $924.16

Third payment of $1000 [after 2 years]:
Using the same formula as above, the present value (PV) of the third payment can be calculated as:
PV = FV / (1+r)^n

In this case, FV = $1000, r = 2% or 0.02, and n = 8 (since there are 8 quarters in 2 years).
PV = $1000 / (1+0.02)^8
PV = $1000 / (1.02)^8
PV ≈ $852.57

Lastly, to find the total present value of the payments, we need to sum up the present values of each payment.
Total Present Value = Present Value of the first payment + Present Value of the second payment + Present Value of the third payment
Total Present Value = $1000 + $924.16 + $852.57
Total Present Value ≈ $2776.73

Therefore, the present value of the payments is approximately $2776.73.