Final answer:
The present value of an ordinary annuity paying $4,000 per year for thirty years at a 6% interest rate is calculated using the present value annuity formula. This allows us to determine the current worth of future payments, which can be understood through an example of calculating a bond's present value using a discount rate.
Step-by-step explanation:
The question asks for the present value of an ordinary annuity of $4,000 per year for thirty years at an annual interest rate of 6.0%. To calculate this, we use the present value annuity formula, which is PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the annual payment, r is the interest rate per period, and n is the number of periods.
Using the provided information, the calculation would be: PV = $4,000 × [(1 - (1 + 0.06)^-30) / 0.06]. This formula considers the time value of money, discounting each payment back to its value in today's dollars.
The concept of present value can be understood through an example of a simple two-year bond. If the bond was issued at $3,000 with an 8% interest rate, the first year's interest would be $240 (3,000 × 8%), and at the end of the second year, the bond would pay $240 in interest plus the $3,000 principal. The present value of such a bond can be calculated using a discount rate, reflecting the bond's worth in today's money considering future payment streams.