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In: Finance

A $ 1 comma 000$1,000 bond with a coupon rate of 5.45.4% paid semiannually has tenten...

A $ 1 comma 000$1,000 bond with a coupon rate of 5.45.4% paid semiannually has tenten years to maturity and a yield to maturity of 88%. If interest rates rise and the yield to maturity increases to 8.38.3%, what will happen to the price of the bond? A. rise by $ 17.79$17.79 B. fall by $ 17.79$17.79 C. fall by $ 21.35$21.35 D. The price of the bond will not change

Solutions

Expert Solution

First scenario:

Information provided:

Future value= $1,000

Time= 10 years*2= 20 semi-annual periods

Coupon rate= 5.4%/2= 2.7% per semi-annual period

Coupon payment= 0.027*1,000= $27

Yield to maturity= 8%/2= 4%

The price of the bond is calculated by entering the below in a financial calculator:

FV= 1,000

N= 20

PMT= 27

I/Y= 4

Press the CPT key and PV to calculate the present value of the bond.

The value obtained is $823.33.

Second scenario when yield to maturity rises to 8.3%.

The price of the bond is calculated by entering the below in a financial calculator:

FV= 1,000

N= 20

PMT= 27

I/Y= 4.15

Press the CPT key and PV to calculate the present value of the bond.

The value obtained is $805.53.

Change in price of the bond when interest rate increases:

= $823.33- $805.53

= $17.80.

Therefore, the price of the bond falls by $17.80 when interest rate increases.

Hence, answer is option b.

In case of any further queries, kindly comment on the solution.

jeff jeffy answered 1 year ago
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