Final answer:
The present value of future cash flows can be calculated using a discount rate. The student's question on the present value of $500 at an 8% interest rate is related to the example of a $3,000 two-year bond at 8%. The present value of this bond at 8% would be exactly $3,000, while recalculations are necessary if the discount rate changes to 11%.
Step-by-step explanation:
The student is asking how to find the present value of a future cash flow when interest rates change. To find the present value of a $500 payment one year in the future with an interest rate of 8%, we can use the following formula:
Present Value = Future Value / (1 + interest rate) ^ number of periods
For the bond example, the present value calculations at two different discount rates are as follows:
8% Discount Rate:
First year interest payment's present value: $240 / (1 + 0.08)¹ = $222.22
Second year interest and principal payment's present value: $3,240 / (1 + 0.08)² = $2,777.78
Total present value at 8% = $222.22 + $2,777.78 = $3,000
11% Discount Rate:
First year interest payment's present value: $240 / (1 + 0.11)¹
Second year interest and principal payment's present value: $3,240 / (1 + 0.11)²
These values must then be calculated to find the present value at 11%.