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# Change in bond prices when interest rate increases

Two bonds have the following criteria:

a. b.
6% coupon 13% coupon
11 yrs to maturity 11 years to maturity
semi annual payments semi annual payments
YTM 9.5% YTM 9.5%

1) If interest rates rise by 1% what is the % change in the price of each bond?
2) If interest rates rise by 4% what is the % change in the price of each bond?

#### Solution Preview

To calculate the price of the bond we need to calculate / read from tables the values of
PVIF= Present Value Interest Factor
PVIFA= Present Value Interest Factor for an Annuity
Price of bond= PVIF * Redemption value + PVIFA * interest payment per period

PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%
PVIF( n, r%)= =1/(1+r%)^n

Bond a

Price of bond
Coupon rate= 6.0%
Face value= \$1,000
Frequency= S Semi Annual
No of years to maturity= 11
No of Periods= 22
Discount rate annually= 9.50% annual
Discount rate per period= 4.75%
n= 22 periods
r= 4.75% per period

Interest payment per period= \$30 Semi Annual
Redemption value= \$1,000

PVIF (22 periods, 4.75% rate)= 0.360256
PVIFA (22 periods, 4.75% rate)= 13.468293

Price of bond=PVIFA X Interest Payment+PVIF X Redemption value
PVIFA X Interest Payment= 404.05 =13.468293*30
PVIF X Redemption value= 360.26 =0.360256*1000
Total= \$764.31 =Price of bond

If interest rate rises by 1%

Price of bond
Coupon rate= 6.0%
Face value= 1000
Frequency= S Semi Annual
No of years to maturity= 11
No ...

#### Solution Summary

Calculates the percentage change in the price of bonds when interest rate increases.

\$2.19