Question

A(n) 17​-year bond has a coupon of 6​% and is priced to yield 9​%. Calculate the price per​ $1,000 par value using​ semi-annual compounding. If an investor purchases this bond two months before a scheduled coupon​ payment, how much accrued interest must be paid to the​ seller?

Answer 1

(a)-Price of the Bond

The Price of the is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $30 [$1,000 x 6% x ½]

Semi-annual Yield to Maturity = 4.50% [9% x ½]

Maturity Period = 34 Years [17 Years x 2]

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $30[PVIFA 4.50%, 34 Years] + $1,000[PVIF 4.50%, 34 Years]

= [$30 x 17.24676] + [$1,000 x 0.22390]

= $517.40 + $223.90

= $741.30

“Therefore, the Price of the Bond = $741.30”

(b)-Accrued Interest to be paid to the seller

Accrued Interest = Semi-annual coupon amount x [4 Months / 6 Months]

= [$1,000 x 6% x ½] x [4 Months / 6 Months]

= $30 x 4/6

= $20.00

“The Accrued Interest to be paid to the seller would be $20.00”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.