Final answer:
To find the percentage change in bond price due to a yield change from 3.5% to 5.8%, one must calculate the bond price at both yields and compare the results. Bond prices are inversely related to yields; thus, the bond price will decrease as the yield increases. The percentage change can be derived by comparing the price at a 3.5% yield to that at a 5.8% yield.
Step-by-step explanation:
To calculate the percentage change in the bond price if the yield changes instantaneously from 3.5% to 5.8%, we need to first calculate the current bond price using the original yield to maturity (YTM) of 3.5%. The bond has a $1,000 par value, a coupon rate of 5%, and 5 years to maturity with annual payments. The present value of the bond's future cash flows can be estimated using the formula for present value of annuities and the present value of a lump sum. Unfortunately, the information provided does not give us the exact current bond price at a YTM of 3.5%. However, we can infer that because the YTM of 3.5% is lower than the coupon rate of 5%, the bond would trade at a premium over its $1,000 par value. To ascertain the percentage change in the bond price when the yield rises to 5.8%, we must use this calculated price and compare it to the new price based on a YTM of 5.8%.
As bond prices and yields are inversely related, an increase in yield would result in a lower bond price. Using the bond pricing formula and comparing the two prices will give us the percentage change. This concept is illustrated by the provided example of the investor who will receive the $1,000 face value, plus $80 for the last year's interest payment. As the interest rate changes, the bond's price adjusts to offer the same expected yield as newly issued bonds with current market rates, showing that the yield, or total return, is a combination of interest payments and capital gains or losses.