Question

A $ 1 comma 000$1,000 bond with a coupon rate of 6.9​% paid semiannually has eight years to maturity and a yield to maturity of 6.6​%.

If interest rates fall and the yield to maturity decreases by​ 0.8%, what will happen to the price of the​ bond?

Answer 1

Information provided:

Future value= $1,000

Coupon rate= 6.9%/2= 3.45% per semi-annual period

Coupon payment= 0.0345*1,000= 34.50

Time= 8 years*2= 16 semi-annual periods

Yield to maturity= 6.6%/2= 3.30% per semi-annual period

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

FV= 1,000

PMT= 34.50

N=16

I/Y= 3.30

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

Therefore, the price of the bond with a yield to maturity of 6.60% is $1,018.42.

The price of the bond when the yield to maturity falls by 0.80% is calculated by entering the below in a financial calculator:

Yield to maturity= 6.60- 0.80= 5.80%. 5.80%/2= 2.90% per semi-annual period.

FV= 1,000

PMT= 34.50

N=16

I/Y= 2.90

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

Therefore, the price of the bond with a yield to maturity of 5.80% is $1,069.62.

Change in the price of the bond= $1,069.62 - $1,018.42 = $51.20.

Therefore, the price of the bond increases by $51.20 when the yield to maturity falls by 0.80%.

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