Question

What is the percentage change in price for a zero coupon bond if the yield changes from 6.5​% to 5.5​%? The bond has a face value of ​$1,000 and it matures in 10 years. Use the price determined from the first​ yield, 6.5​%, as the base in the percentage calculation.

Answer 1

Price of the bond with 6.5% yield:

Information provided:

Face value= future value= $1,000

Time= 10 years

Yield to maturity= 6.5%

The price of the bond is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

I/Y= 6.5

N= 10

Press the CPT key and PV to compute the present value.

The value obtained is 532.73.

Therefore, the price of the bond is $532.73.

Price of the bond with 5.5% yield:

Information provided:

Face value= future value= $1,000

Time= 10 years

Yield to maturity= 5.5%

The price of the bond is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

I/Y= 5.5

N= 10

Press the CPT key and PV to compute the present value.

The value obtained is 585.43.   

Therefore, the price of the bond is $585.43.

Percentage change in price: New price - old price/ old price

= $585.43 - $532.73/ $532.73

= $52.70/ $532.73

= 0.0989*100

= 9.89%.

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