offers a 6.3 percent bond with a current market price of $767.50. The yield to maturity is 8.49 percent. The face value is $1,000. Interest is paid semiannually. How many years is it until this bond matures

9.25 years

Explanation:

Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond. Price of the bond is calculated by following formula:

According to given data

Assuming the Face value of the bond is $1,000

Coupon payment = C = $1,000 x 6.3 = $63 annually = $31.5 semiannually

Current Yield = r = 8.49% / 2 = 4.245% semiannually

Market value = $767.50

Market Value of the Bond = $31.5 x [ (1 - (1 + 4.425%) ^-n) / 4.425% ] + [ $1,000 / (1 + 4.425%) ^n ]

Market Value of the Bond = $31.5 x [ (1 - (1 + 4.425%) ^-n) / 4.425% ] + [ $1,000 / (1 + 4.425%) ^n ]

n = 18.53 / 2

n = 9.25 years

27.85years

Explanation:

Nper = ? (indicates the period)

PV = 767.50 (indicates the price)

FV = 1000 (indicates the face value)

Rate = 8.49%/2 (indicates semi-annual YTM)

PMT = 1000 x 6.30% x 1/2 = 31.50 (indicates the amount of interest payment)

Period = Nper (Rate, PMT, PV, FV) / 2 = Nper (8.49%/2,31.50,-767.50,1000) / 2 = 27.85 Years