Final answer:
Without the bond's modified duration, it is not possible to calculate the exact percentage change in the price of a 13-year zero coupon bond if interest rates increase by 77 basis points. However, we can say that a bond's price will decrease when interest rates rise, reflecting a discount needed to make the bond's lower interest payments attractive compared to newer issues.
Step-by-step explanation:
The question is asking to estimate the percentage change in the price of a 13-year zero coupon bond if interest rates rise by 77 basis points. However, to accurately answer this, we need the bond's modified duration, which is not provided. Modified duration is an essential figure that measures the price sensitivity of a bond to a change in interest rates. Without this information, we cannot provide the exact percentage change.
To give an understanding of the concept using a simpler example, let's look at a 2-year bond with a face value of $3,000 and an interest rate of 8%. The bond would pay $240 in interest each year, based on the formula ($3,000 x 8%). At an 8% discount rate, using the present value calculation, we would discount each interest payment and the principal to find the present value of all future cash flows. If the discount rate increases to 11%, due to an increase in interest rates, the present value of these cash flows would decrease, reflecting the reduced attractiveness of the bond compared to new bonds issued at the higher prevailing rates.