Final answer:
The present value of a bond can be calculated using the present value formula, considering the interest payments and principal repayment. Changes in the market interest rate affect the present value of the bond. Similarly, the price of a bond is lower than its face value when its interest rate is less than the market interest rate.
Step-by-step explanation:
The task involves calculating the present value of the tuition expenses and the duration of the financial obligation at a given bond yield rate. It also includes finding the duration of a zero-coupon bond. These calculations require an understanding of financial mathematics and the use of the present value formula to find the current worth of future cash flows.
Using a similar example, let's consider a two-year bond with a principal amount of $3,000 and an interest rate of 8%. The bond pays $240 in interest at the end of the first year and $240 in interest plus the $3,000 principal at the end of the second year. To find the present value of the bond when the discount rate is 8%, we use the formula:
- Present Value of Year 1 Interest = $240 / (1 + 0.08)^1 = $222.22
- Present Value of Year 2 Payments = $3,240 / (1 + 0.08)^2 = $2,777.78
Summing these up gives us the bond's present value at an 8% discount rate as $3,000. If interest rates rise to 11%, the new present values would be:
- Present Value of Year 1 Interest = $240 / (1 + 0.11)^1
- Present Value of Year 2 Payments = $3,240 / (1 + 0.11)^2
The calculations for the 11% discount rate need to be completed to provide the updated present value.
When the bond's interest rate is less than the market interest rate, the price of the bond will be lower than its face value. For example, if a bond is expected to pay $1,080 in a year, and the current market interest rate is 12%, you wouldn't pay more than $964 for it because $964 growing at 12% for one year equals $1,080.