Final answer:
All statements offered in the student's question are correct: compound interest exceeds simple interest with positive rates, present value decreases as the discount rate increases, and present value can be derived from the future value formula. The concepts also relate to how bond prices are affected by changes in interest rates.
Step-by-step explanation:
The student's question pertains to various concepts related to interest rates, present value, and future value in financial calculations. Specifically, the correct statement among the provided options is (d) None of the above, as all the statements given are indeed correct. Statement (a) is true because compound interest will accrue to a higher amount than simple interest if the rate of return is greater than zero. For statement (b), it is accurate that the present value of annuities or perpetuities will be lower if the discount rate is higher because the future cash inflows are discounted more. Finally, statement (c) is also true because the present value formula is a reorganization of the future value formula, which conceptually reflects the time value of money by adjusting future cash flows to their value in today's terms. Furthermore, when applying these concepts to bonds, we see that if the interest rate decreases after a bond is issued, the bond will sell for more than its face value. Conversely, if the interest rate increases, the bond will sell for less because its locked-in rate becomes less attractive compared to new available rates. The impact of fluctuating interest rates is reflected in the bond's present value, which decreases as the discount rate increases due to the higher opportunity cost of capital.