# Calculate the price of a bond given various interest rates.

A bond has a face value of $100, a coupon rate of 8% and 5 years to redemption at par. The annual interest payment has just been made.

(a) What is the price of the bond if market interest rates are;

(i) 6%

(ii) 7%

(iii) 8%

(iv) 10%

(b) What is the duration of the bond if market interest rates are 7%?

(c) What will be the change in value of the bond for a 1% change in market interest rates?

#### Solution Preview

Price of bond given various interest rates has been calculated using a HP 10BII financial calculator as follows:

(ai) Market interest rate = 6%

N = 5 (years to maturity)

FV = 100 (face value in pounds)

PMT = 8 (interest payment in pound, 8% coupon rate of face value)

I/Y = 6 (in percent, market interest rate)

Compute current price PV = 108.42 (in pounds)

(aii) Market interest rate = 7%

N = 5 (years to maturity)

FV = 100 (face value in pounds)

PMT = 8 (interest payment in pound, 8% coupon rate of face value)

I/Y = 7 (in percent, market interest rate)

Compute current price PV = 104.10 (in pounds)

(aiii) Market interest rate = 8%

N = 5 (years to maturity)

FV = 100 (face value in pounds)

PMT = 8 (interest payment in pound, 8% coupon rate ...

#### Solution Summary

This solution shows the calculation of the current price of the bond, assuming several different market interest rates, using a financial calculator. The solution also shows how to calculate the duration of the bond, using the duration formula and explaining how to solve the duration using Excel functions.