Question

Bond A pays $4,000 in 14 years. Bond B pays $4,000 in 28 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 5 percent.

Using the rule of 70, the value of Bond A is approximately (250, 500, 1,000, 2,000, 4,000)  , and the value of Bond B is approximately (250, 500, 1,000, 2,000, 4,000) .

Now suppose the interest rate increases to 10 percent.

Using the rule of 70, the value of Bond A is now approximately (250, 500, 1,000, 2,000, 4,000) , and the value of Bond B is approximately (250, 500, 1,000, 2,000, 4,000)   .

Comparing each bond’s value at 5 percent versus 10 percent, Bond A’s value decreases by a (smaller, larger)   percentage than Bond B’s value.

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

Answer 1

Given that Bond A pays $4,000 in 14 years and Bond B pays $4,000 in 28 years, and that the interest rate is 5 percent, we see that Using the rule of 70, the value of Bond A is 70/5 = doubled after 14 years. Now if its value is 4000 in 14 years, its current value must be halved. Hence the value is 2000.

Sinilarly the value of Bond B is approximately one fourth now because it pays 4000 in 28 years. Hence its value is 4000/4 = 1000.

Now suppose the interest rate increases to 10 percent. Hence the doubling time is 70/10 = 7 years

Using the rule of 70, the value of Bond A is now approximately 1,000 and the value of Bond B is 250

Comparing each bond’s value at 5 percent versus 10 percent, Bond A’s value decreases by a smaller 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.