A perpetual bond sells for $1,000 and will pay $98 a year forever. The Fed changes its policy and the interest rate changes to 19 percent. The price of the bond is now---.
To determine the price of the bond after the interest rate change, we need to calculate the present value of the perpetuity using the formula:
Present Value = Annual Payment / Interest Rate
Given:
Annual Payment = $98
Interest Rate = 19% or 0.19
Present Value = $98 / 0.19 = $515.79
Therefore, the price of the bond after the interest rate change is $515.79.
To calculate the new price of the bond after the change in interest rate, we can use the formula for the price of a perpetuity:
Price of perpetuity = Annual payment / Interest rate
In this case, the annual payment is $98, and the interest rate has changed to 19%. Converting 19% to decimal form, we have an interest rate of 0.19.
Price of perpetuity = $98 / 0.19
Using a calculator, we can determine the new price of the bond:
Price of perpetuity = $98 / 0.19 = $515.79
Therefore, the new price of the bond is approximately $515.79.