On February 5, 2018, Breanna purchased a newly issued three-year bond that has a face value...

On February 5, 2018, Breanna purchased a newly issued three-year bond that has a face value for $1,000 and a coupon rate of 6.5%. On February 6, 2018, the market rate on similar bonds rose to 7.2%. If Breanna sold her bond, what price would she have received? Show your work using the present value/future value formula.

Expert Solution

Price of the Bond

Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the Face Value

Face Value of the bond = $1,000

Annual Coupon Amount = $65 [$1,000 x 6.50%]

Annual Yield to Maturity = 7.20%

Maturity Period = 3 Years

Therefore, The Price of the Bond = Present Value of the Coupon Payments + Present Value of the Face Value

= $65[PVIFA 7.20%, 3 Years] + $1,000[PVIF 7.20%, 3 Years]

= [$65 x 2.61476] + [$1,000 x 0.81174]

= $169.96 + $811.74

= $981.70

“Therefore, If Breanna sold her bond, she would have received $981.70”

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.

jeff jeffy answered 1 year ago

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