# 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?

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#### 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% ...

#### 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.

Zero Coupon Bonds: Calculating Price, Interest, and Value

1) You purchased a zero-coupon bond that has a face value of $1,000, five years to maturity and a yield to maturity of 7.3%. It is one year later and similar bonds are offering a yield to maturity of 8.1%. You will sell the bond now. You have a tax rate of 40% on regular income and 15% on capital gains. Calculate the following for this bond.

a) The purchase price of the bond

b) The current price of the bond

c) The imputed interest income

d) The capital gain (or loss) on the bond

e) The before-tax rate of return on this investment

f) The after-tax rate of return on this investment

2) You have purchased a bond for $973.02. The bond has a coupon rate of 6.4%, pays interest annually, has a face value of $1,000, 4 years to maturity, and a yield to maturity of 7.2%. The bond's duration is 3.6481 years. You expect that interest rates will fall by .3% later today.

* Use the modified duration to find the approximate percentage change in the bond's price. Find the new price of the bond from this calculation.

* Use your calculator to do the regular present value calculations to find the bond's new price at its new yield to maturity.

* What is the amount of the difference between the two answers?

Why are your answers different? Explain the reason in words and illustrate it graphically.

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