Final answer:
The present value (PV) of future payments of $5,000 can be calculated using the formula PV = FV / (1 + r)^n for each specified interest rate and time period. Similarly, the PV of receiving $15,000 in eight or six years at a 9 percent discount rate can be computed. Such calculations highlight the impact of the interest rate and timing on the present worth of future money.
Step-by-step explanation:
Present Value Calculations
To determine the present value of receiving $5,000 in the future under different interest rates and time periods, we use the present value formula:
PV = FV / (1 + r)^n
Where:
- PV = Present Value
- FV = Future Value ($5,000 in these scenarios)
- r = Annual discount/interest rate (expressed as a decimal)
- n = Number of years until payment is received
For each scenario:
5 percent for ten years: PV = $5,000 / (1 + 0.05)^10
- 7 percent for seven years: PV = $5,000 / (1 + 0.07)^7
- 9 percent for four years: PV = $5,000 / (1 + 0.09)^4
The present value of $15,000 to be received in eight years at a discount rate of 9 percent is calculated as:
PV = $15,000 / (1 + 0.09)^8
If you had to wait six years instead of eight to receive the $15,000, the calculation would be:
PV = $15,000 / (1 + 0.09)^6
It's important to note that as interest rate risks change, so does the present value. An example is given with a two-year bond issued at $3,000 with an 8% interest rate. The present values change when recalculating with discount rates of 8% and 11%.
By adding up the present values of different time periods and at varying interest rates, you can see how the discount rate and time until receipt affect how much future payments are worth today.