Question
Asked Nov 6, 2019
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What must be the price of a $2,000 bond with a 5.7% coupon rate, annual coupons, and 30 years to maturity if YTM is 9.3% APR?

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Expert Answer

Step 1

The price of a bond consists present value of all future coupon payments and the redemption payment.

It is given that,

Number of years is 30.

Face value is $2,000.

Coupon rate is 5.7%. So, coupon payment will be ($2,000 × 5.7%) = $114.

Yield to maturity is 9.3%.

Step 2

The below expression can be used to calculate the price of bond.

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1-(1+i) Face value Bond price Coup on paymentx (1+1) i Here is interest rate nis number of years

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Step 3

Substitute $114 for coupon payment, 9.3% for i, 30 for n and $...

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1-(1+9.3%) 30 $2,000 + Bond price $114x| 9.3% (1+9.3%0 0.93059 $2,000 $114x 0.093 14.408 =$114x10.006 +$138.81 $1,140.72 $138.82 $1,279.54

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