Final answer:
The present value of an annuity formula calculates the value today of a series of future payments at a given discount rate. Using the formula PV = PMT / (1+r)^n, one can sum the present values of all individual payments to find the total present value of the annuity.
Step-by-step explanation:
The student's question asks for the present value of a series of future payments under a given discount rate. To calculate this, we utilize the present value of an annuity formula. The payments ($7,100 per year) start in three years and end in 25 years, making it 23 payments in total. The discount rate is 7%. The present value of each individual payment can be calculated using the formula: PV = PMT / (1+r)^n, where PV is the present value, PMT is the annual payment, r is the discount rate, and n is the number of years until the payment is received. The present value of the annuity is the sum of the present values of all individual payments.
To provide an example of a simpler calculation involving present value, let us consider a two-year bond paying 8% interest on a principal of $3,000. The bond pays $240 interest at the end of each year and returns the principal in the second year. The present value at an 8% discount rate is computed as follows: $240/(1+0.08)¹ = $222.20 for the first payment and $3,240/(1+0.08)² = $2,777.80 for the second payment, totaling $3,000. If the discount rate increases to 11%, the present values will decrease accordingly, showing how present value is sensitive to changes in the discount rate.