Question

Bond A pays $8,000 in 20 years. Bond B pays $8,000 in 10 years. (To keep things simple, assume these are zero-coupon bonds, which means the $8,000 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.

Answer 1

Answer:

To find the value of bond, let's use the formula:

Value of bond = price of bond / (1 + interest rate)ⁿ

Here n represents number of years.

At 7% interest rate:

Value of bond A = $\frac{8000}{(1+0.07)^2^0} = 2067.35$

Value of bond B = $\frac{8000}{(1+0.07)^1^0} = 4066.79$

At 14% interest rate:

Value of bond A = $= \frac{8000}{(1+0.14)^20} = 582.09$

Value of bond B = $= \frac{8000}{(1+0.14)^10} = 2157.95$

The difference between bond A at 7% and 14%:

$582.09 - $2067.35 = -$1485.26

The difference between bond B at 7% and 14%:

$2157.95 - $4066.79 = -$1908.84

% decrease between bond A and B:

$\frac{1908.84 - 1485.26}{1908.84} * 100 = 22.19$

Therefore, from the above calculations, we have the following:

Suppose the interest rate is 7%, Using the rule of 70, the value of Bond A is approximately $2067.35, and the value of Bond B is approximately $4066.79 .

Now suppose the interest rate increases to 14 percent.

Using the rule of 70, the value of Bond A is now approximately $528.09 , and the value of Bond B is approximately $2157.95 .

Comparing each bond's value at 7 percent versus 14 percent, Bond A's value decreases by a 22.19 percentage than Bond B's value.

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.