Attempts: 3. Problems and Applications Q3 Bond A pays $12,000 in 14 years. Bond
ID: 2564125 • Letter: A
Question
Attempts: 3. Problems and Applications Q3 Bond A pays $12,000 in 14 years. Bond B pays $12,000 in 28 years. (To keep things simple, assume these are zero-coupon bonds, which means the Average: /4 $12,000 is the only payment the bondholder receives.) Suppose the interest rate is 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 10 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 5 percent versus 10 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 rateExplanation / Answer
1. Interest rate = 5%
Value of bond A = $12000 x (1/1.05)14
= $12000 x 0.5050679
= $6061
Value of bond B = $12000 x (1/1.05)28
= $12000 x 0.2550936
= $3061
2. Interest rate = 10%
Value of bond A = $12000 x (1/1.10)14
= $12000 x 0.26333125
= $3160
Value of bond B = $12000 x (1/1.10)28
= $12000 x 0.0693433
= $832
3.
Bond A's value at 5% interest rate = $6061
Bond A's value at 10% interest rate = $3160
Percentage decrease in Bond A's value = ($6061 - $3160)/ $6061 = 47.86%
Bond A's value decreases by a 47.86% than Bond B's value.
4.
The value of a bond decreases 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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