Bond A pays $4,000 in 10 years. Bond B pays $4,000 in 20 years. (To keep...

Bond A pays $4,000 in 10 years. Bond B pays $4,000 in 20 years. (To keep things simple, assume these are zero-coupon bonds, which means the $4,000 is the only payment the bondholder receives.)

Suppose the interest rate is 7 percent.

Using the rule of 70, the value of Bond A is approximately ? , and the value of Bond B is approximately ? .

Now suppose the interest rate increases to 14 percent.

Using the rule of 70, the value of Bond A is now approximately ? , and the value of Bond B is approximately ? .

Comparing each bond’s value at 7 percent versus 14 percent, Bond A’s value decreases by a percentage than Bond B’s value.

The value of a bond ? when the interest rate increases, and bonds with a longer time to maturity are ? sensitive to changes in the interest rate.

Expert Solution

Suppose the interest rate is 7 %:

According to rule 70, if interest rate is 7%, the value of bond will double in 70 / 7 = 10 years. Thus, the value of bond A today is $2000 because the value will double once in 10 years. And the value of bond B today is $1000 because the value will double twice in 20 years.

Using the rule of 70, the value of Bond A is approximately $2000 , and the value of Bond B is approximately $1000

Suppose the interest rate is 14%:

According to rule 70, if interest rate is 14%, the value of bond will double in 70 / 14 = 5 years. Thus, the value of bond A today is $1000 because the value will double twice in 10 years. And the value of bond B today is $250 because the value will double four times in 20 years..

Using the rule of 70, the value of Bond A is approximately $1000 , and the value of Bond B is approximately $250

The % change in value for Bond A = (1000 ? 2000) / 2000 * 100 = ?50%
The % change in value for Bond B = (250 - 1000) / 1000 * 100 = -75%

Comparing each bond’s value at 7 percent versus 14 percent, Bond A’s value decreases by a 25% (i.e. 75% - 50%) percentage than Bond B’s value.

The value of a bond falls when the interest rate increases, and bonds with a longer time to maturity are more sensitive to changes in the interest rate.

Rahul Sunny answered 2 years ago

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