# 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?

1. There is an inverse relationship between bond prices and interest rates.
2. There is a direct relationship between bond prices and interest rates.
3. 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)
4. 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)

## 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:

1. 8.7 years
2. 7.6 years
3. 7.1 years
4. 6.5 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?

1. 10%
2. 5.8%
3. 8.7%
4. None of the above