Question

A $1,000 bond with a coupon rate of 6.1​% paid semiannually has five years to maturity and a yield to maturity of 9​%. If interest rates rise and the yield to maturity increases to 9.3​%, what will happen to the price of the​ bond?

A. rise by $ 10.94

B. fall by $ 13.13

C. fall by $ 10.94

D. The price of the bond will not change

Answer 1

1.Yield to maturity at 9%.

Information provided:

Future value= $1,000

Time= 5 years*2= 10 semi-annual periods

Coupon rate= 6.1%/2= 3.05%

Coupon payment= 0.0305*1,000= $30.50 per semi-annual period

Yield to maturity= 9%/2= 4.50%

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

The present value is computed by entering the below in a financial calculator:

FV= 1,000

N= 10

PMT= 30.50

I/Y= 4.50

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

The value obtained is 885.2656.

Therefore, the price of the bond when the yield to maturity is 9% is $885.27.

2.Yield to maturity at 9.3%.

Information provided:

Future value= $1,000

Time= 5 years*2= 10 semi-annual periods

Coupon rate= 6.1%/2= 3.05%

Coupon payment= 0.0305*1,000= $30.50 per semi-annual period

Yield to maturity= 9.3%/2= 4.65%

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

The present value is computed by entering the below in a financial calculator:

FV= 1,000

N= 10

PMT= 30.50

I/Y= 4.65

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

The value obtained is 874.3251.

Therefore, the price of the bond when the yield to maturity is 9% is $874.33.

Hence, with an increase in interest rate, the price of the bond $885.27- $874.33= 10.9449 falls by $10.9 4.

Hence, the answer is option c.

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