Final answer:
The present value of 7 equal yearly payments of $2,688 starting 4 years from now, with a 4% annual interest rate, can be calculated using the present value formula for an annuity. Similar present value calculations with different discount rates for a two-year bond show the impact of interest rate risk and how payments are valued in today's terms.
Step-by-step explanation:
To calculate the present value of a court settlement with 7 equal yearly payments of $2,688, starting 4 years from now, and an annual interest rate of 4%, we will use the present value formula for an annuity. Each payment needs to be discounted to its present value, and then summed up to get the total present value of the settlement. The formula for the present value of an annuity is: PVA = PMT [((1-(1+r)^(-n))/r)], where PVA is the present value of the annuity, PMT is the payment amount, r is the discount rate per period, and n is the number of periods. In this case, r is 0.04, PMT is $2,688, and n is 7. However, we have to adjust our calculation to account for the fact that payments start 4 years from now.
To illustrate a similar present value calculation, consider a two-year bond issued for $3,000 with an interest rate of 8%. It pays $240 in interest at the end of the first year and $3,240 (including principal) at the end of the second year. If the discount rate is 8%, the present value for the first payment is $240/(1+0.08) = $222.22, and the second is $3,240/(1+0.08)² = $2,777.78, summing up to a total present value of $3,000.
If we increase the discount rate to 11%, the present value for the first payment now is $240/(1+0.11) = $216.22, and the second is $3,240/(1+0.11)² = $2,630.63, for a lower total present value due to higher interest rates. These examples demonstrate the impact of interest rate risk and show how future payments can be valued in today's terms through the present value formula.