Final answer:
The present value of an asset yielding $500 in five years and $1,000 in ten years at a 6% discount rate is approximately $931.88. This is calculated by discounting each future cash flow back to its present value and summing the two.
Step-by-step explanation:
To calculate the present value of an asset that yields $500 in five years and $1,000 in ten years with a discount rate of 6%, we apply the present value formula:
- Present Value (PV) = Future Value (FV) / (1 + r)^n
For the $500 payment in five years:
- PV = $500 / (1 + 0.06)^5
- PV = $500 / (1.3382)
- PV ≈ $373.49
For the $1,000 payment in ten years:
- PV = $1,000 / (1 + 0.06)^10
- PV = $1,000 / (1.7908)
- PV ≈ $558.39
The total present value of both payments is the sum of the two individual present values:
- Total PV = PV of $500 + PV of $1,000
- Total PV = $373.49 + $558.39
- Total PV ≈ $931.88
This calculation illustrates the concept of present discounted value, a financial principle that determines the value today of a sum of money to be received in the future, adjusted for interest or discount rate. The same principle applied to a simple two-year bond demonstrates the impact of varying interest rates on the present value of future cash flows.