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In: Economics

3. Problems and Applications Q3 Bond A pays $12,000 in 40 years. Bond B pays $12,000...

3. Problems and Applications Q3

Bond A pays $12,000 in 40 years. Bond B pays $12,000 in 20 years. (To keep things simple, assume these are zero-coupon bonds, which means the $12,000 is the only payment the bondholder receives.)

Suppose the interest rate is 3.5 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 7 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 3.5 percent versus 7 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.

Solutions

Expert Solution

Suppose the interest rate is 3.5 percent.

Using the rule of 70, the value of Bond A is approximately $3000, and the value of Bond B is approximately $6000.

Explanation:

Usinf rule 70, the bond value will double in 70 / 3.5 = 20 years. So, in 40 years the bond A will double twice. So, the current value of bond A = $12000 / 4 = $3000. And, in 20 years the bond A will double once. So, the current value of bond B = $12000 / 2 = $6000

Suppose the interest rate increases to 7 percent.

Using the rule of 70, the value of Bond A is now approximately $750 , and the value of Bond B is approximately $3000.

Explanation:

Usinf rule 70, the bond value will double in 70 / 7 = 10 years. So, in 40 years the bond A will double four times. So, the current value of bond A = $12000 / 16 = $750. And, in 20 years the bond A will double twice. So, the current value of bond B = $12000 / 4 = $3000.

Comparing each bond’s value at 3.5 percent versus 7 percent, Bond A’s value decreases by a 25 percentage than Bond B’s value.

Explanation:

% decrease in value of bond A = [(3000 - 750) / 3000] * 100 = 75%

% decrease in value of bond A = [(6000 - 3000) / 6000] * 100 = 50%

So, Bond A’s value decreases by 25% (i.e. 75% - 50%) 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.


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