Final answer:
The present discounted value of a debt of $124,500 due 4 years from now with a 3.25% interest rate compounded quarterly is approximately $109,604.89. The compound discount is the difference between the future and present values, totaling $14,895.11.
Step-by-step explanation:
To calculate the present discounted value and the compound discount of a debt of $124,500 due 4 years from now at a 3.25% interest rate compounded quarterly, we use the present value formula:
PV = FV / (1 + r/n)nt
Where:
- PV is the present value
- FV is the future value ($124,500)
- r is the annual interest rate (3.25% or 0.0325)
- n is the number of times the interest is compounded per year (quarterly compounding, so n=4)
- t is the number of years (t=4)
Plugging the values into the formula, we get:
PV = $124,500 / (1 + 0.0325/4)4×4
PV = $124,500 / (1 + 0.008125)16
PV ≈ $124,500 / (1.135892)
PV ≈ $109,604.89
The present value of the debt is approximately $109,604.89 and the compound discount is the difference between the future value and the present value, which is $124,500 - $109,604.89 = $14,895.11.