Question

A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 8.8%, and sells for $1,120. Interest is paid annually. (Assume a face value of $1,000 and annual coupon payments.)

a. If the bond has a yield to maturity of 9.2% 1 year from now, what will its price be at that time? (Do not round intermediate calculations. Round your answer to nearest whole number.)
b. What will be the rate of return on the bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.)
c. If the inflation rate during the year is 3%, what is the real rate of return on the bond? (Assume annual interest payments.) (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.)

Answer 1

The price of the bond 1 year from now will be approximately $1,108. The rate of return on the bond will be approximately 1.58%. The real rate of return on the bond, adjusted for inflation, will be approximately -0.0146%.

Step-by-step explanation:

The price of the bond 1 year from now can be calculated using the formula:

Price of the bond = [(Coupon payment / (1 + Yield to maturity))^Time to maturity] + (Face value / (1 + Yield to maturity))^Time to maturity

Using the given values, we can calculate the price of the bond 1 year from now as follows:

Price of the bond = [(88 / (1 + 0.092))^9] + (1000 / (1 + 0.092))^9

Performing the calculations, the price of the bond 1 year from now will be approximately $1,108.

The rate of return on the bond can be calculated using the formula:

Rate of return = [(Price of the bond / Face value)^(1 / Time to maturity)] - 1

Using the given values, we can calculate the rate of return on the bond as follows:

Rate of return = [(1120 / 1000)^(1 / 10)] - 1

Performing the calculations, the rate of return on the bond will be approximately 1.58%.

The real rate of return on the bond, adjusted for inflation, can be calculated using the formula:

Real rate of return = [(1 + Rate of return) / (1 + Inflation rate)] - 1

Using the given values, we can calculate the real rate of return on the bond as follows:

Real rate of return = [(1 + 0.0158) / (1 + 0.03)] - 1

Performing the calculations, the real rate of return on the bond will be approximately -0.0146%.