Answer
a) Bond A: 4,000 dollars; Bond B: 2,000 dollars
b) Bond A: 2,000 dollars; Bond B: 500 dollars. Bond A decreases by 50%, and Bond B decreases by 75%.
c) falls; more
Work Step by Step
a)
Bond A
8000 dollars due in 20 years, interest rate of 3.5%
Rule of 70 says that 70 divided by the interest rate (as a number, not a decimal) would provide the number of years required to double the value of the bond.
$70/3.5 = 20$
Since the bond would double once in 20 years, we see that the present value of the bond is $8000/2$, or 4000 dollars.
Bond B
8000 dollars due in 40 years, interest rate of 3.5%
$70/3.5 =20$
Since the bond is due in 40 years, and we know the value doubles in 20 years, we can see that the value of the bond would double $40/20$, or two times. Thus, the present value of the bond is $8000/2^2$, or 2000 dollars.
b)
Bond A
8000 dollars due in 20 years, interest rate of 7%
Rule of 70 says that 70 divided by the interest rate (as a number, not a decimal) would provide the number of years required to double the value of the bond.
$70/7 = 10$
Since the bond would double once in 10 years, we see that the bond will double twice ($20/10$). Thus, we see that the present value of the bond is $8000/2^2$, or 2000 dollars.
Bond B
8000 dollars due in 40 years, interest rate of 7%
$70/7 =10$
Since the bond is due in 40 years, and we know the value doubles in 10 years, we can see that the value of the bond would double $40/10$, or four times. Thus, the present value of the bond is $8000/2^4$, or 500 dollars.
Decreases
Bond A:
$(4000-2000)/4000$
$2000/4000$
$2/4$
$.50$
$50%$
Bond B:
$(4000-1000)/4000$
$3000/4000$
$.75$
$75%$
