# Bond Price and Interest Rate

Consider two bonds A and B. The coupon rates are 10 percent and the face values are $1,000 for both bonds. Both bonds have annual coupons. Bond A has 20 years to maturity while bond B has 10 years of maturity.

a. What are the prices of the two bonds if the relevant market interest rate for both bonds is 10 percent?

b. If the market interest rate increases to 12 percent, what will be the prices of the two bond?

c. If the market interest rate decreases to 8 percent, what will be the prices of the two bonds?

https://brainmass.com/business/interest-rates/64260

#### Solution Preview

Consider two bonds A and B. The coupon rates are 10 percent and the face values are $1,000 for both bonds. Both bonds have annual coupons. Bond A has 20 years to maturity while bond B has 10 years of maturity.

a. What are the prices of the two bonds if the relevant market interest rate for both bonds is 10 percent

b. If the market interest rate increases to 12 percent, what will be the prices of the two bond

c. If the market interest rate decreases to 8 percent, what will be the prices of the two bonds?

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

market interest rate = 10%

Price of bond A

Coupon rate= 10.000%

Face value= $1,000

Frequency= A Annual

No of years to maturity= 20

No of Periods= 20

Discount rate annually= 10.00% annual

Discount rate per period= 10.00%

n= 20 periods

r= 10.00% per period

Interest payment per period= $100 Annual

Redemption value= 1000

PVIF ...

#### Solution Summary

Calculates bond price for different interest rates.

Advance bond concepts

Problem:

5.Calculate the effective duration of a bond to a 100 basis point change in interest rates with a 6-1/4 coupon, 10-years remaining to maturity, and an asking quote of 110.7811 (decimal, not 32nds).

Calculate the effective convexity to a 100 basis point change of the bond in Question 5.

Calculate the total percentage price change (duration and convexity) to a 65 basis point decrease in interest rates for the bond in Questions 5 and 6.

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