# Relationship between Interest Rates and Bond Prices

Classified in Mathematics

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Which of the following statements about the relationship between interest rates and bond prices is true?

- There is an inverse relationship between bond prices and interest rates.
- There is a direct relationship between bond prices and interest rates.
- The price of short-term bonds fluctuates more than the price of long-term bonds for a given change in interest rates. (Assuming that coupon rate is the same for both)
- The price of long-term bonds fluctuates more than the price of short-term bonds for a given change in interest rates. (Assuming that the coupon rate is the same for both)

**Answer:** I and IV only

## Bond Duration

Consider a bond with a face value of $1,000, a coupon rate of 8%, a yield to maturity of 9%, and ten years to maturity. This bond's duration is:

- 8.7 years
- 7.6 years
- 7.1 years
- 6.5 years

**Answer:** 7.1 years

PV = $865.80; Duration = [(73.39) + 2(67.33) + 3(61.77) + 4(56.67) + 5(51.99) + 6(47.70) + 7(43.76) + 8(40.15) + 9(36.83) + 10(33.79)]/(935.82) = 7.1 years

## Real Rate of Interest

If the nominal interest rate per year is 12% and the inflation rate is 3%, what is the real rate of interest?

- 10%
- 5.8%
- 8.7%
- None of the above

**Answer:** 8.7%

1 + r_{real} = (1 + r_{nominal})/(1 + r_{inflation}) = 1.12/1.03 = 1.087; r_{real} = 8.7%

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